LMFDB - Embedded newform 315.2.bh.c.169.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [315,2,Mod(169,315)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(315, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4, 3, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("315.169");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 315 = 3^{2} \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	315.bh (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$2.51528766367$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			169.20
Character	$\chi$	$=$	315.169
Dual form			315.2.bh.c.274.20

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.719518 + 0.415414i) q^{2} +(-1.08800 + 1.34768i) q^{3} +(-0.654862 - 1.13425i) q^{4} +(-2.03156 + 0.934211i) q^{5} +(-1.34268 + 0.517712i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.74981i q^{8} +(-0.632505 - 2.93256i) q^{9} +O(q^{10})$	\(q+(0.719518 + 0.415414i) q^{2} +(-1.08800 + 1.34768i) q^{3} +(-0.654862 - 1.13425i) q^{4} +(-2.03156 + 0.934211i) q^{5} +(-1.34268 + 0.517712i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.74981i q^{8} +(-0.632505 - 2.93256i) q^{9} +(-1.84983 - 0.171758i) q^{10} +(0.813674 - 1.40932i) q^{11} +(2.24111 + 0.351523i) q^{12} +(-4.28497 + 2.47393i) q^{13} +(-0.415414 - 0.719518i) q^{14} +(0.951323 - 3.75433i) q^{15} +(-0.167413 + 0.289968i) q^{16} -6.45735i q^{17} +(0.763130 - 2.37279i) q^{18} -7.27402 q^{19} +(2.39003 + 1.69253i) q^{20} +(1.61608 - 0.623128i) q^{21} +(1.17091 - 0.676023i) q^{22} +(2.44296 - 1.41044i) q^{23} +(3.70588 + 2.99180i) q^{24} +(3.25450 - 3.79582i) q^{25} -4.11082 q^{26} +(4.64034 + 2.33822i) q^{27} +1.30972i q^{28} +(-2.54087 + 4.40091i) q^{29} +(2.24410 - 2.30612i) q^{30} +(0.485008 + 0.840058i) q^{31} +(-5.00373 + 2.88890i) q^{32} +(1.01405 + 2.62992i) q^{33} +(2.68248 - 4.64619i) q^{34} +(2.22649 + 0.206732i) q^{35} +(-2.91207 + 2.63785i) q^{36} +11.7481i q^{37} +(-5.23379 - 3.02173i) q^{38} +(1.32798 - 8.46641i) q^{39} +(2.56890 + 5.58642i) q^{40} +(2.24906 + 3.89549i) q^{41} +(1.42165 + 0.222990i) q^{42} +(-8.11350 - 4.68433i) q^{43} -2.13138 q^{44} +(4.02461 + 5.36680i) q^{45} +2.34367 q^{46} +(-1.71295 - 0.988971i) q^{47} +(-0.208640 - 0.541106i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.91851 - 1.37919i) q^{50} +(8.70247 + 7.02561i) q^{51} +(5.61212 + 3.24016i) q^{52} -8.60079i q^{53} +(2.36748 + 3.61005i) q^{54} +(-0.336424 + 3.62328i) q^{55} +(-1.37491 + 2.38141i) q^{56} +(7.91415 - 9.80309i) q^{57} +(-3.65640 + 2.11103i) q^{58} +(0.259322 + 0.449159i) q^{59} +(-4.88135 + 1.37952i) q^{60} +(1.92279 - 3.33037i) q^{61} +0.805916i q^{62} +(-0.918517 + 2.85593i) q^{63} -4.13071 q^{64} +(6.39401 - 9.02900i) q^{65} +(-0.362883 + 2.31353i) q^{66} +(-3.22570 + 1.86236i) q^{67} +(-7.32428 + 4.22868i) q^{68} +(-0.757112 + 4.82691i) q^{69} +(1.51612 + 1.07366i) q^{70} -1.38612 q^{71} +(-8.06400 + 1.73927i) q^{72} -9.06190i q^{73} +(-4.88032 + 8.45297i) q^{74} +(1.57466 + 8.51589i) q^{75} +(4.76348 + 8.25060i) q^{76} +(-1.40932 + 0.813674i) q^{77} +(4.47257 - 5.54008i) q^{78} +(-2.59833 + 4.50044i) q^{79} +(0.0692192 - 0.745488i) q^{80} +(-8.19987 + 3.70972i) q^{81} +3.73717i q^{82} +(-2.41970 - 1.39701i) q^{83} +(-1.76509 - 1.42498i) q^{84} +(6.03253 + 13.1185i) q^{85} +(-3.89188 - 6.74093i) q^{86} +(-3.16657 - 8.21249i) q^{87} +(-3.87538 - 2.23745i) q^{88} +10.7409 q^{89} +(0.666335 + 5.53339i) q^{90} +4.94785 q^{91} +(-3.19961 - 1.84729i) q^{92} +(-1.65982 - 0.260347i) q^{93} +(-0.821665 - 1.42317i) q^{94} +(14.7776 - 6.79547i) q^{95} +(1.55073 - 9.88658i) q^{96} +(1.87765 + 1.08406i) q^{97} +0.830828i q^{98} +(-4.64759 - 1.49475i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	$ 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) $ 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/315\mathbb{Z}\right)^\times$.

$n$	$127$	$136$	$281$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.719518	+	0.415414i	0.508776	+	0.293742i	0.732331	−	0.680949i	$-0.238433\pi$
$2$	0.719518	+	0.415414i	0.508776	+	0.293742i	−0.223554	+	0.974692i	$0.571766\pi$
$3$	−1.08800	+	1.34768i	−0.628158	+	0.778086i
$3$	−1.08800	+	1.34768i	−0.628158	+	0.778086i
$4$	−0.654862	−	1.13425i	−0.327431	−	0.567127i
$5$	−2.03156	+	0.934211i	−0.908543	+	0.417792i
$5$	−2.03156	+	0.934211i	−0.908543	+	0.417792i
$6$	−1.34268	+	0.517712i	−0.548149	+	0.211355i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$		−	2.74981i		−	0.972206i
$9$	−0.632505	−	2.93256i	−0.210835	−	0.977522i
$10$	−1.84983	−	0.171758i	−0.584968	−	0.0543148i
$11$	0.813674	−	1.40932i	0.245332	−	0.424927i	−0.716893	−	0.697183i	$-0.754436\pi$
$11$	0.813674	−	1.40932i	0.245332	−	0.424927i	0.962225	+	0.272256i	$0.0877697\pi$
$12$	2.24111	+	0.351523i	0.646952	+	0.101476i
$13$	−4.28497	+	2.47393i	−1.18844	+	0.686144i	−0.957951	−	0.286932i	$-0.907364\pi$
$13$	−4.28497	+	2.47393i	−1.18844	+	0.686144i	−0.230485	+	0.973076i	$0.574031\pi$
$14$	−0.415414	−	0.719518i	−0.111024	−	0.192299i
$15$	0.951323	−	3.75433i	0.245631	−	0.969363i
$16$	−0.167413	+	0.289968i	−0.0418533	+	0.0724920i
$17$		−	6.45735i		−	1.56614i	−0.621935	−	0.783069i	$-0.713653\pi$
$17$		−	6.45735i		−	1.56614i	0.621935	−	0.783069i	$-0.286347\pi$
$18$	0.763130	−	2.37279i	0.179871	−	0.559271i
$19$	−7.27402			−1.66878			−0.834388	−	0.551178i	$-0.814179\pi$
$19$	−7.27402			−1.66878			−0.834388	+	0.551178i	$0.814179\pi$
$20$	2.39003	+	1.69253i	0.534426	+	0.378461i
$21$	1.61608	−	0.623128i	0.352657	−	0.135978i
$22$	1.17091	−	0.676023i	0.249638	−	0.144129i
$23$	2.44296	−	1.41044i	0.509393	−	0.294098i	−0.223191	−	0.974775i	$-0.571647\pi$
$23$	2.44296	−	1.41044i	0.509393	−	0.294098i	0.732584	+	0.680677i	$0.238314\pi$
$24$	3.70588	+	2.99180i	0.756459	+	0.610699i
$25$	3.25450	−	3.79582i	0.650900	−	0.759163i
$26$	−4.11082			−0.806197
$27$	4.64034	+	2.33822i	0.893033	+	0.449990i
$28$			1.30972i			0.247515i
$29$	−2.54087	+	4.40091i	−0.471827	+	0.817229i	−0.999480	−	0.0322309i	$-0.989739\pi$
$29$	−2.54087	+	4.40091i	−0.471827	+	0.817229i	0.527653	+	0.849460i	$0.323072\pi$
$30$	2.24410	−	2.30612i	0.409714	−	0.421037i
$31$	0.485008	+	0.840058i	0.0871100	+	0.150879i	0.906288	−	0.422660i	$-0.138904\pi$
$31$	0.485008	+	0.840058i	0.0871100	+	0.150879i	−0.819178	+	0.573539i	$0.805570\pi$
$32$	−5.00373	+	2.88890i	−0.884543	+	0.510691i
$33$	1.01405	+	2.62992i	0.176523	+	0.457811i
$34$	2.68248	−	4.64619i	0.460041	−	0.796814i
$35$	2.22649	+	0.206732i	0.376346	+	0.0349440i
$36$	−2.91207	+	2.63785i	−0.485345	+	0.439641i
$37$			11.7481i			1.93137i	0.259709	+	0.965687i	$0.416373\pi$
$37$			11.7481i			1.93137i	−0.259709	+	0.965687i	$0.583627\pi$
$38$	−5.23379	−	3.02173i	−0.849034	−	0.490190i
$39$	1.32798	−	8.46641i	0.212647	−	1.35571i
$40$	2.56890	+	5.58642i	0.406179	+	0.883290i
$41$	2.24906	+	3.89549i	0.351244	+	0.608373i	0.986468	−	0.163955i	$-0.0524253\pi$
$41$	2.24906	+	3.89549i	0.351244	+	0.608373i	−0.635223	+	0.772328i	$0.719092\pi$
$42$	1.42165	+	0.222990i	0.219366	+	0.0344081i
$43$	−8.11350	−	4.68433i	−1.23730	−	0.714354i	−0.268757	−	0.963208i	$-0.586613\pi$
$43$	−8.11350	−	4.68433i	−1.23730	−	0.714354i	−0.968541	+	0.248854i	$0.919946\pi$
$44$	−2.13138			−0.321317
$45$	4.02461	+	5.36680i	0.599953	+	0.800035i
$46$	2.34367			0.345556
$47$	−1.71295	−	0.988971i	−0.249859	−	0.144256i	0.369841	−	0.929095i	$-0.379412\pi$
$47$	−1.71295	−	0.988971i	−0.249859	−	0.144256i	−0.619700	+	0.784839i	$0.712746\pi$
$48$	−0.208640	−	0.541106i	−0.0301145	−	0.0781019i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	3.91851	−	1.37919i	0.554161	−	0.195048i
$51$	8.70247	+	7.02561i	1.21859	+	0.983782i
$52$	5.61212	+	3.24016i	0.778261	+	0.449329i
$53$		−	8.60079i		−	1.18141i	−0.806888	−	0.590705i	$-0.798850\pi$
$53$		−	8.60079i		−	1.18141i	0.806888	−	0.590705i	$-0.201150\pi$
$54$	2.36748	+	3.61005i	0.322173	+	0.491266i
$55$	−0.336424	+	3.62328i	−0.0453634	+	0.488562i
$56$	−1.37491	+	2.38141i	−0.183730	+	0.318229i
$57$	7.91415	−	9.80309i	1.04825	−	1.29845i
$58$	−3.65640	+	2.11103i	−0.480109	+	0.277191i
$59$	0.259322	+	0.449159i	0.0337609	+	0.0584756i	0.882412	−	0.470477i	$-0.155918\pi$
$59$	0.259322	+	0.449159i	0.0337609	+	0.0584756i	−0.848651	+	0.528953i	$0.822585\pi$
$60$	−4.88135	+	1.37952i	−0.630180	+	0.178096i
$61$	1.92279	−	3.33037i	0.246188	−	0.426410i	−0.716277	−	0.697816i	$-0.754155\pi$
$61$	1.92279	−	3.33037i	0.246188	−	0.426410i	0.962465	+	0.271406i	$0.0874886\pi$
$62$			0.805916i			0.102351i
$63$	−0.918517	+	2.85593i	−0.115722	+	0.359813i
$64$	−4.13071			−0.516339
$65$	6.39401	−	9.02900i	0.793079	−	1.11991i
$66$	−0.362883	+	2.31353i	−0.0446678	+	0.284776i
$67$	−3.22570	+	1.86236i	−0.394082	+	0.227523i	−0.683927	−	0.729550i	$-0.739729\pi$
$67$	−3.22570	+	1.86236i	−0.394082	+	0.227523i	0.289845	+	0.957073i	$0.406396\pi$
$68$	−7.32428	+	4.22868i	−0.888200	+	0.512802i
$69$	−0.757112	+	4.82691i	−0.0911456	+	0.581091i
$70$	1.51612	+	1.07366i	0.181211	+	0.128327i
$71$	−1.38612			−0.164502			−0.0822508	−	0.996612i	$-0.526211\pi$
$71$	−1.38612			−0.164502			−0.0822508	+	0.996612i	$0.526211\pi$
$72$	−8.06400	+	1.73927i	−0.950352	+	0.204975i
$73$		−	9.06190i		−	1.06061i	−0.847805	−	0.530307i	$-0.822076\pi$
$73$		−	9.06190i		−	1.06061i	0.847805	−	0.530307i	$-0.177924\pi$
$74$	−4.88032	+	8.45297i	−0.567326	+	0.982637i
$75$	1.57466	+	8.51589i	0.181826	+	0.983331i
$76$	4.76348	+	8.25060i	0.546409	+	0.946408i
$77$	−1.40932	+	0.813674i	−0.160607	+	0.0927268i
$78$	4.47257	−	5.54008i	0.506419	−	0.627291i
$79$	−2.59833	+	4.50044i	−0.292335	+	0.506339i	−0.974361	−	0.224989i	$-0.927765\pi$
$79$	−2.59833	+	4.50044i	−0.292335	+	0.506339i	0.682027	+	0.731327i	$0.261099\pi$
$80$	0.0692192	−	0.745488i	0.00773894	−	0.0833481i
$81$	−8.19987	+	3.70972i	−0.911097	+	0.412192i
$82$			3.73717i			0.412701i
$83$	−2.41970	−	1.39701i	−0.265596	−	0.153342i	0.361289	−	0.932454i	$-0.382337\pi$
$83$	−2.41970	−	1.39701i	−0.265596	−	0.153342i	−0.626885	+	0.779112i	$0.715670\pi$
$84$	−1.76509	−	1.42498i	−0.192588	−	0.155478i
$85$	6.03253	+	13.1185i	0.654320	+	1.42290i
$86$	−3.89188	−	6.74093i	−0.419672	−	0.726893i
$87$	−3.16657	−	8.21249i	−0.339492	−	0.880471i
$88$	−3.87538	−	2.23745i	−0.413117	−	0.238513i
$89$	10.7409			1.13853			0.569267	−	0.822153i	$-0.307227\pi$
$89$	10.7409			1.13853			0.569267	+	0.822153i	$0.307227\pi$
$90$	0.666335	+	5.53339i	0.0702379	+	0.583271i
$91$	4.94785			0.518676
$92$	−3.19961	−	1.84729i	−0.333582	−	0.192594i
$93$	−1.65982	−	0.260347i	−0.172116	−	0.0269968i
$94$	−0.821665	−	1.42317i	−0.0847483	−	0.146788i
$95$	14.7776	−	6.79547i	1.51615	−	0.697201i
$96$	1.55073	−	9.88658i	0.158271	−	1.00904i
$97$	1.87765	+	1.08406i	0.190646	+	0.110070i	0.592285	−	0.805728i	$-0.298226\pi$
$97$	1.87765	+	1.08406i	0.190646	+	0.110070i	−0.401639	+	0.915798i	$0.631559\pi$
$98$			0.830828i			0.0839263i
$99$	−4.64759	−	1.49475i	−0.467100	−	0.150228i
$100$	−6.43667	−	1.20570i	−0.643667	−	0.120570i
$101$	8.32942	−	14.4270i	0.828809	−	1.43554i	−0.0701646	−	0.997535i	$-0.522352\pi$
$101$	8.32942	−	14.4270i	0.828809	−	1.43554i	0.898973	−	0.438003i	$-0.144314\pi$
$102$	3.34305	+	8.67019i	0.331011	+	0.858476i
$103$	1.08308	−	0.625319i	0.106720	−	0.0616145i	−0.445690	−	0.895187i	$-0.647042\pi$
$103$	1.08308	−	0.625319i	0.106720	−	0.0616145i	0.552410	+	0.833573i	$0.313708\pi$
$104$	6.80283	+	11.7829i	0.667073	+	1.15540i
$105$	−2.70103	+	2.77568i	−0.263594	+	0.270879i
$106$	3.57289	−	6.18843i	0.347030	−	0.601073i
$107$		−	7.25745i		−	0.701604i	−0.936450	−	0.350802i	$-0.885909\pi$
$107$		−	7.25745i		−	0.701604i	0.936450	−	0.350802i	$-0.114091\pi$
$108$	−0.386647	−	6.79453i	−0.0372051	−	0.653804i
$109$	2.18289			0.209083			0.104542	−	0.994521i	$-0.466662\pi$
$109$	2.18289			0.209083			0.104542	+	0.994521i	$0.466662\pi$
$110$	−1.74722	+	2.46726i	−0.166591	+	0.235244i
$111$	−15.8327	−	12.7819i	−1.50277	−	1.21321i
$112$	0.289968	−	0.167413i	0.0273994	−	0.0158191i
$113$	−3.28661	+	1.89753i	−0.309179	+	0.178504i	−0.646559	−	0.762864i	$-0.723793\pi$
$113$	−3.28661	+	1.89753i	−0.309179	+	0.178504i	0.337380	+	0.941368i	$0.390459\pi$
$114$	9.76672	−	3.76585i	0.914737	−	0.352704i
$115$	−3.64538	+	5.14765i	−0.339933	+	0.480021i
$116$	6.65567			0.617964
$117$	9.96521	+	11.0012i	0.921284	+	1.01706i
$118$			0.430905i			0.0396680i
$119$	−3.22868	+	5.59223i	−0.295972	+	0.512639i
$120$	−10.3237	−	2.61596i	−0.942421	−	0.238803i
$121$	4.17587	+	7.23282i	0.379624	+	0.657529i
$122$	2.76697	−	1.59751i	0.250509	−	0.144632i
$123$	−7.69687	−	1.20727i	−0.694003	−	0.108856i
$124$	0.635227	−	1.10024i	0.0570450	−	0.0988049i
$125$	−3.06563	+	10.7518i	−0.274198	+	0.961673i
$126$	−1.84728	+	1.67333i	−0.164569	+	0.149072i
$127$		−	16.9697i		−	1.50582i	−0.658125	−	0.752909i	$-0.728650\pi$
$127$		−	16.9697i		−	1.50582i	0.658125	−	0.752909i	$-0.271350\pi$
$128$	7.03533	+	4.06185i	0.621841	+	0.359020i
$129$	15.1405	−	5.83788i	1.33305	−	0.513996i
$130$	8.35138	−	3.84037i	0.732465	−	0.336823i
$131$	−9.39321	−	16.2695i	−0.820688	−	1.42147i	−0.905170	−	0.425049i	$-0.860257\pi$
$131$	−9.39321	−	16.2695i	−0.820688	−	1.42147i	0.0844818	−	0.996425i	$-0.473077\pi$
$132$	2.31894	−	2.87242i	0.201838	−	0.250012i
$133$	6.29949	+	3.63701i	0.546235	+	0.315369i
$134$	−3.09460			−0.267333
$135$	−11.6115	−	0.415186i	−0.999361	−	0.0357335i
$136$	−17.7565			−1.52261
$137$	5.59538	+	3.23049i	0.478046	+	0.276000i	0.719602	−	0.694387i	$-0.244324\pi$
$137$	5.59538	+	3.23049i	0.478046	+	0.276000i	−0.241556	+	0.970387i	$0.577658\pi$
$138$	−2.54992	+	3.15853i	−0.217064	+	0.268872i
$139$	−6.92754	−	11.9989i	−0.587586	−	1.01773i	−0.994548	−	0.104284i	$-0.966745\pi$
$139$	−6.92754	−	11.9989i	−0.587586	−	1.01773i	0.406961	−	0.913445i	$-0.366588\pi$
$140$	−1.22356	−	2.66079i	−0.103410	−	0.224878i
$141$	3.19651	−	1.23251i	0.269195	−	0.103796i
$142$	−0.997335	−	0.575812i	−0.0836945	−	0.0483211i
$143$			8.05188i			0.673332i
$144$	0.956240	+	0.307544i	0.0796867	+	0.0256286i
$145$	1.05056	−	11.3144i	0.0872439	−	0.939613i
$146$	3.76444	−	6.52020i	0.311547	−	0.539616i
$147$	−1.71113	−	0.268395i	−0.141132	−	0.0221368i
$148$	13.3253	−	7.69338i	1.09533	−	0.632392i
$149$	−0.499136	−	0.864529i	−0.0408908	−	0.0708249i	0.844856	−	0.534994i	$-0.179686\pi$
$149$	−0.499136	−	0.864529i	−0.0408908	−	0.0708249i	−0.885746	+	0.464169i	$0.846353\pi$
$150$	−2.40463	+	6.78148i	−0.196337	+	0.553705i
$151$	0.581647	−	1.00744i	0.0473338	−	0.0819845i	−0.841388	−	0.540432i	$-0.818261\pi$
$151$	0.581647	−	1.00744i	0.0473338	−	0.0819845i	0.888722	+	0.458447i	$0.151594\pi$
$152$			20.0022i			1.62239i
$153$	−18.9366	+	4.08431i	−1.53093	+	0.330197i
$154$	−1.35205			−0.108951
$155$	−1.77012	−	1.25353i	−0.142179	−	0.100686i
$156$	−10.4727	+	4.03807i	−0.838488	+	0.323304i
$157$	−9.29951	+	5.36907i	−0.742182	+	0.428499i	−0.822862	−	0.568241i	$-0.807624\pi$
$157$	−9.29951	+	5.36907i	−0.742182	+	0.428499i	0.0806803	+	0.996740i	$0.474291\pi$
$158$	−3.73909	+	2.15876i	−0.297466	+	0.171742i
$159$	11.5912	+	9.35768i	0.919238	+	0.742112i
$160$	7.46655	−	10.5435i	0.590282	−	0.833539i
$161$	−2.82089			−0.222317
$162$	−7.44103	−	0.737129i	−0.584623	−	0.0579143i
$163$			6.03397i			0.472617i	0.971678	+	0.236308i	$0.0759376\pi$
$163$			6.03397i			0.472617i	−0.971678	+	0.236308i	$0.924062\pi$
$164$	2.94565	−	5.10202i	0.230017	−	0.398400i
$165$	−4.51700	−	4.39552i	−0.351648	−	0.342191i
$166$	−1.16068	−	2.01035i	−0.0900860	−	0.156034i
$167$	−1.54140	+	0.889927i	−0.119277	+	0.0688646i	−0.558452	−	0.829537i	$-0.688604\pi$
$167$	−1.54140	+	0.889927i	−0.119277	+	0.0688646i	0.439174	+	0.898402i	$0.355271\pi$
$168$	−1.71349	−	4.44391i	−0.132198	−	0.342855i
$169$	5.74062	−	9.94304i	0.441586	−	0.764849i
$170$	−1.10910	+	11.9450i	−0.0850645	+	0.916141i
$171$	4.60086	+	21.3315i	0.351836	+	1.63126i
$172$			12.2704i			0.935607i
$173$	9.11568	+	5.26294i	0.693052	+	0.400134i	0.804754	−	0.593608i	$-0.202297\pi$
$173$	9.11568	+	5.26294i	0.693052	+	0.400134i	−0.111702	+	0.993742i	$0.535630\pi$
$174$	1.13318	−	7.22448i	0.0859059	−	0.547686i
$175$	−4.71639	+	1.66002i	−0.356525	+	0.125486i
$176$	0.272440	+	0.471879i	0.0205359	+	0.0355692i
$177$	−0.887468	−	0.139202i	−0.0667062	−	0.0104630i
$178$	7.72828	+	4.46192i	0.579259	+	0.334435i
$179$	−20.6820			−1.54585			−0.772923	−	0.634499i	$-0.781206\pi$
$179$	−20.6820			−1.54585			−0.772923	+	0.634499i	$0.781206\pi$
$180$	3.45175	−	8.07944i	0.257278	−	0.602206i
$181$	9.97025			0.741083			0.370541	−	0.928816i	$-0.379172\pi$
$181$	9.97025			0.741083			0.370541	+	0.928816i	$0.379172\pi$
$182$	3.56007	+	2.05541i	0.263890	+	0.152357i
$183$	2.39629	+	6.21476i	0.177139	+	0.459408i
$184$	−3.87846	−	6.71769i	−0.285924	−	0.495234i
$185$	−10.9752	−	23.8670i	−0.806912	−	1.75474i
$186$	−1.08612	−	0.876838i	−0.0796382	−	0.0642929i
$187$	−9.10051	−	5.25418i	−0.665495	−	0.384224i
$188$			2.59056i			0.188936i
$189$	−2.84954	−	4.34513i	−0.207274	−	0.316061i
$190$	13.4557	+	1.24937i	0.976181	+	0.0906392i
$191$	−9.45013	+	16.3681i	−0.683788	+	1.18435i	0.290029	+	0.957018i	$0.406335\pi$
$191$	−9.45013	+	16.3681i	−0.683788	+	1.18435i	−0.973816	+	0.227337i	$0.926998\pi$
$192$	4.49422	−	5.56690i	0.324343	−	0.401756i
$193$	10.6291	−	6.13672i	0.765101	−	0.441731i	−0.0660234	−	0.997818i	$-0.521031\pi$
$193$	10.6291	−	6.13672i	0.765101	−	0.441731i	0.831124	+	0.556087i	$0.187698\pi$
$194$	0.900669	+	1.56000i	0.0646643	+	0.112002i
$195$	5.21154	+	18.4407i	0.373206	+	1.32056i
$196$	0.654862	−	1.13425i	0.0467759	−	0.0810182i
$197$		−	16.2775i		−	1.15972i	−0.814715	−	0.579862i	$-0.803107\pi$
$197$		−	16.2775i		−	1.15972i	0.814715	−	0.579862i	$-0.196893\pi$
$198$	−2.72309	−	3.00617i	−0.193521	−	0.213639i
$199$	−21.6571			−1.53523			−0.767616	−	0.640910i	$-0.778557\pi$
$199$	−21.6571			−1.53523			−0.767616	+	0.640910i	$0.778557\pi$
$200$	−10.4378	−	8.94927i	−0.738063	−	0.632809i
$201$	0.999695	−	6.37347i	0.0705130	−	0.449550i
$202$	11.9863	−	6.92032i	0.843357	−	0.486912i
$203$	4.40091	−	2.54087i	0.308884	−	0.178334i
$204$	2.26991	−	14.4716i	0.158926	−	1.01322i
$205$	−8.20832	−	5.81283i	−0.573294	−	0.405986i
$206$	1.03907			0.0723952
$207$	−5.68140	−	6.27203i	−0.394885	−	0.435936i
$208$		−	1.65667i		−	0.114869i
$209$	−5.91868	+	10.2515i	−0.409404	+	0.709109i
$210$	−3.09650	+	0.875107i	−0.213679	+	0.0603881i
$211$	−9.86419	−	17.0853i	−0.679079	−	1.17620i	−0.975259	−	0.221067i	$-0.929046\pi$
$211$	−9.86419	−	17.0853i	−0.679079	−	1.17620i	0.296180	−	0.955132i	$-0.404287\pi$
$212$	−9.75549	+	5.63233i	−0.670010	+	0.386830i
$213$	1.50810	−	1.86805i	0.103333	−	0.127996i
$214$	3.01485	−	5.22187i	0.206091	−	0.356960i
$215$	20.8592	+	1.93680i	1.42259	+	0.132089i
$216$	6.42966	−	12.7601i	0.437483	−	0.868212i
$217$		−	0.970016i		−	0.0658490i
$218$	1.57063	+	0.906805i	0.106377	+	0.0614166i
$219$	12.2126	+	9.85936i	0.825249	+	0.666234i
$220$	4.33003	−	1.99116i	0.291930	−	0.134244i
$221$	15.9750	+	27.6695i	1.07460	+	1.86125i
$222$	−6.08213	−	15.7740i	−0.408206	−	1.05868i
$223$	−10.6300	−	6.13725i	−0.711839	−	0.410981i	0.0999024	−	0.994997i	$-0.468147\pi$
$223$	−10.6300	−	6.13725i	−0.711839	−	0.410981i	−0.811742	+	0.584017i	$0.801480\pi$
$224$	5.77781			0.386046
$225$	−13.1900	−	7.14316i	−0.879331	−	0.476211i
$226$	−3.15304			−0.209737
$227$	11.9760	+	6.91432i	0.794872	+	0.458920i	0.841675	−	0.539985i	$-0.181570\pi$
$227$	11.9760	+	6.91432i	0.794872	+	0.458920i	−0.0468029	+	0.998904i	$0.514903\pi$
$228$	−16.3019	−	2.55699i	−1.07962	−	0.169341i
$229$	0.326856	+	0.566131i	0.0215992	+	0.0374110i	0.876623	−	0.481178i	$-0.159791\pi$
$229$	0.326856	+	0.566131i	0.0215992	+	0.0374110i	−0.855024	+	0.518589i	$0.826458\pi$
$230$	−4.76132	+	2.18949i	−0.313952	+	0.144370i
$231$	0.436772	−	2.78460i	0.0287375	−	0.183213i
$232$	12.1017	+	6.98691i	0.794515	+	0.458713i
$233$		−	2.60596i		−	0.170722i	−0.996350	−	0.0853611i	$-0.972796\pi$
$233$		−	2.60596i		−	0.170722i	0.996350	−	0.0853611i	$-0.0272044\pi$
$234$	2.60011	+	12.0552i	0.169975	+	0.788075i
$235$	4.40387	+	0.408903i	0.287277	+	0.0266739i
$236$	0.339641	−	0.588275i	0.0221087	−	0.0382934i
$237$	−3.23818	−	8.39821i	−0.210342	−	0.545522i
$238$	−4.64619	+	2.68248i	−0.301167	+	0.173879i
$239$	13.3769	+	23.1695i	0.865282	+	1.49871i	0.866767	+	0.498713i	$0.166194\pi$
$239$	13.3769	+	23.1695i	0.865282	+	1.49871i	−0.00148521	+	0.999999i	$0.500473\pi$
$240$	0.929372	+	0.904378i	0.0599907	+	0.0583773i
$241$	−9.99074	+	17.3045i	−0.643560	+	1.11468i	0.341072	+	0.940037i	$0.389210\pi$
$241$	−9.99074	+	17.3045i	−0.643560	+	1.11468i	−0.984632	+	0.174642i	$0.944123\pi$
$242$			6.93886i			0.446047i
$243$	3.92194	−	15.0870i	0.251593	−	0.967833i
$244$	−5.03665			−0.322438
$245$	−1.82483	−	1.29228i	−0.116584	−	0.0825608i
$246$	−5.03652	−	4.06604i	−0.321117	−	0.259241i
$247$	31.1689	−	17.9954i	1.98323	−	1.14502i
$248$	2.31000	−	1.33368i	0.146685	−	0.0846888i
$249$	4.51536	−	1.74103i	0.286150	−	0.110334i
$250$	−6.67224	+	6.46263i	−0.421990	+	0.408733i
$251$	−10.5147			−0.663680			−0.331840	−	0.943336i	$-0.607669\pi$
$251$	−10.5147			−0.663680			−0.331840	+	0.943336i	$0.607669\pi$
$252$	3.84085	−	0.828407i	0.241951	−	0.0521848i
$253$		−	4.59057i		−	0.288607i
$254$	7.04945	−	12.2100i	0.442322	−	0.766124i
$255$	−24.2430	−	6.14303i	−1.51816	−	0.384692i
$256$	7.50542	+	12.9998i	0.469088	+	0.812485i
$257$	−17.7466	+	10.2460i	−1.10700	+	0.639127i	−0.938051	−	0.346498i	$-0.887371\pi$
$257$	−17.7466	+	10.2460i	−1.10700	+	0.639127i	−0.168949	+	0.985625i	$0.554037\pi$
$258$	13.3190	+	2.08912i	0.829205	+	0.130063i
$259$	5.87404	−	10.1741i	0.364995	−	0.632190i
$260$	−14.4284	−	1.33969i	−0.894810	−	0.0830838i
$261$	14.5131	+	4.66766i	0.898337	+	0.288921i
$262$		−	15.6083i		−	0.964283i
$263$	9.43669	+	5.44827i	0.581891	+	0.335955i	0.761885	−	0.647713i	$-0.224274\pi$
$263$	9.43669	+	5.44827i	0.581891	+	0.335955i	−0.179993	+	0.983668i	$0.557608\pi$
$264$	7.23180	−	2.78844i	0.445086	−	0.171616i
$265$	8.03495	+	17.4731i	0.493583	+	1.07336i
$266$	3.02173	+	5.23379i	0.185274	+	0.320905i
$267$	−11.6861	+	14.4753i	−0.715179	+	0.885877i
$268$	4.22477	+	2.43917i	0.258069	+	0.148996i
$269$	5.33793			0.325460			0.162730	−	0.986671i	$-0.447970\pi$
$269$	5.33793			0.325460			0.162730	+	0.986671i	$0.447970\pi$
$270$	−8.18224	−	5.12233i	−0.497955	−	0.311735i
$271$	−7.26974			−0.441605			−0.220803	−	0.975319i	$-0.570868\pi$
$271$	−7.26974			−0.441605			−0.220803	+	0.975319i	$0.570868\pi$
$272$	1.87243	+	1.08105i	0.113533	+	0.0655481i
$273$	−5.38327	+	6.66814i	−0.325810	+	0.403574i
$274$	2.68399	+	4.64880i	0.162146	+	0.280844i
$275$	−2.70144	−	7.67521i	−0.162903	−	0.462832i
$276$	5.97074	−	2.30220i	0.359397	−	0.138576i
$277$	3.98827	+	2.30263i	0.239632	+	0.138352i	0.615008	−	0.788521i	$-0.289153\pi$
$277$	3.98827	+	2.30263i	0.239632	+	0.138352i	−0.375376	+	0.926873i	$0.622486\pi$
$278$		−	11.5112i		−	0.690395i
$279$	2.15676	−	1.95366i	0.129122	−	0.116962i
$280$	0.568473	−	6.12243i	0.0339728	−	0.365885i
$281$	2.29184	−	3.96959i	0.136720	−	0.236806i	−0.789533	−	0.613708i	$-0.789677\pi$
$281$	2.29184	−	3.96959i	0.136720	−	0.236806i	0.926253	+	0.376902i	$0.123011\pi$
$282$	2.81195	+	0.441062i	0.167449	+	0.0262648i
$283$	−18.2562	+	10.5402i	−1.08522	+	0.626549i	−0.932299	−	0.361690i	$-0.882200\pi$
$283$	−18.2562	+	10.5402i	−1.08522	+	0.626549i	−0.152917	+	0.988239i	$0.548867\pi$
$284$	0.907714	+	1.57221i	0.0538629	+	0.0932933i
$285$	−6.91995	+	27.3091i	−0.409902	+	1.61765i
$286$	−3.34486	+	5.79347i	−0.197786	+	0.342575i
$287$		−	4.49812i		−	0.265516i
$288$	11.6368	+	12.8465i	0.685704	+	0.756988i
$289$	−24.6974			−1.45279
$290$	5.45607	−	7.70453i	0.320392	−	0.452426i
$291$	−3.50386	+	1.35102i	−0.205400	+	0.0791981i
$292$	−10.2785	+	5.93429i	−0.601504	+	0.347278i
$293$	8.14488	−	4.70245i	0.475829	−	0.274720i	−0.242848	−	0.970064i	$-0.578081\pi$
$293$	8.14488	−	4.70245i	0.475829	−	0.274720i	0.718677	+	0.695344i	$0.244748\pi$
$294$	−1.11969	−	0.903943i	−0.0653019	−	0.0527190i
$295$	−0.946439	−	0.670234i	−0.0551038	−	0.0390226i
$296$	32.3050			1.87769
$297$	7.07103	−	4.63720i	0.410303	−	0.269077i
$298$		−	0.829392i		−	0.0480454i
$299$	−6.97867	+	12.0874i	−0.403587	+	0.699033i
$300$	8.62801	−	7.36280i	0.498138	−	0.425092i
$301$	4.68433	+	8.11350i	0.270000	+	0.467655i
$302$	0.837012	−	0.483249i	0.0481646	−	0.0278079i
$303$	10.3806	+	26.9220i	0.596350	+	1.54663i
$304$	1.21777	−	2.10924i	0.0698438	−	0.120973i
$305$	−0.795003	+	8.56215i	−0.0455217	+	0.490267i
$306$	−15.3219	−	4.92780i	−0.875896	−	0.281704i
$307$		−	1.80317i		−	0.102913i	−0.998675	−	0.0514563i	$-0.983614\pi$
$307$		−	1.80317i		−	0.102913i	0.998675	−	0.0514563i	$-0.0163863\pi$
$308$	1.84583	+	1.06569i	0.105176	+	0.0607232i
$309$	−0.335665	+	2.14000i	−0.0190953	+	0.121741i
$310$	−0.752896	−	1.63727i	−0.0427616	−	0.0929907i
$311$	−2.70204	−	4.68008i	−0.153219	−	0.265383i	0.779190	−	0.626788i	$-0.215631\pi$
$311$	−2.70204	−	4.68008i	−0.153219	−	0.265383i	−0.932409	+	0.361405i	$0.882297\pi$
$312$	−23.2811	−	3.65169i	−1.31803	−	0.206736i
$313$	21.6702	+	12.5113i	1.22487	+	0.707179i	0.965952	−	0.258720i	$-0.0833007\pi$
$313$	21.6702	+	12.5113i	1.22487	+	0.707179i	0.258918	+	0.965899i	$0.416634\pi$
$314$	−8.92156			−0.503473
$315$	−0.802013	−	6.66009i	−0.0451883	−	0.375253i
$316$	6.80619			0.382878
$317$	−12.7673	−	7.37121i	−0.717084	−	0.414009i	0.0965945	−	0.995324i	$-0.469205\pi$
$317$	−12.7673	−	7.37121i	−0.717084	−	0.414009i	−0.813678	+	0.581315i	$0.802538\pi$
$318$	4.45274	+	11.5481i	0.249697	+	0.647588i
$319$	4.13488	+	7.16182i	0.231509	+	0.400985i
$320$	8.39181	−	3.85896i	0.469116	−	0.215722i
$321$	9.78075	+	7.89612i	0.545908	+	0.440718i
$322$	−2.02968	−	1.17184i	−0.113110	−	0.0653039i
$323$			46.9710i			2.61353i
$324$	9.57756	+	6.87139i	0.532087	+	0.381744i
$325$	−4.55485	+	24.3163i	−0.252658	+	1.34883i
$326$	−2.50660	+	4.34155i	−0.138828	+	0.240456i
$327$	−2.37499	+	2.94185i	−0.131337	+	0.162685i
$328$	10.7119	−	6.18450i	0.591464	−	0.341482i
$329$	0.988971	+	1.71295i	0.0545238	+	0.0944379i
$330$	−1.42410	−	5.03909i	−0.0783943	−	0.277393i
$331$	−6.25138	+	10.8277i	−0.343607	+	0.595145i	−0.985100	−	0.171984i	$-0.944982\pi$
$331$	−6.25138	+	10.8277i	−0.343607	+	0.595145i	0.641493	+	0.767129i	$0.278316\pi$
$332$			3.65940i			0.200836i
$333$	34.4520	−	7.43073i	1.88796	−	0.407201i
$334$	−1.47875			−0.0809138
$335$	4.81338	−	6.79698i	0.262983	−	0.371359i
$336$	−0.0898657	+	0.572931i	−0.00490258	+	0.0312560i
$337$	−22.2621	+	12.8531i	−1.21270	+	0.700150i	−0.963346	−	0.268263i	$-0.913550\pi$
$337$	−22.2621	+	12.8531i	−1.21270	+	0.700150i	−0.249350	+	0.968413i	$0.580217\pi$
$338$	8.26096	−	4.76947i	0.449337	−	0.259425i
$339$	1.01857	−	6.49383i	0.0553213	−	0.352696i
$340$	10.9293	−	15.4332i	0.592723	−	0.836985i
$341$	1.57855			0.0854834
$342$	−5.55103	+	17.2597i	−0.300165	+	0.933298i
$343$		−	1.00000i		−	0.0539949i
$344$	−12.8810	+	22.3106i	−0.694499	+	1.20291i
$345$	−2.97123	−	10.5135i	−0.159965	−	0.566026i
$346$	4.37260	+	7.57356i	0.235072	+	0.407157i
$347$	12.8815	−	7.43714i	0.691515	−	0.399246i	−0.112664	−	0.993633i	$-0.535938\pi$
$347$	12.8815	−	7.43714i	0.691515	−	0.399246i	0.804179	+	0.594387i	$0.202605\pi$
$348$	−7.24138	+	8.96975i	−0.388179	+	0.480829i
$349$	1.03220	−	1.78782i	0.0552522	−	0.0956996i	−0.837076	−	0.547086i	$-0.815737\pi$
$349$	1.03220	−	1.78782i	0.0552522	−	0.0956996i	0.892329	+	0.451386i	$0.149070\pi$
$350$	−4.08313	−	0.764837i	−0.218252	−	0.0408823i
$351$	−25.6683	+	1.46067i	−1.37007	+	0.0779647i
$352$			9.40251i			0.501155i
$353$	−7.43108	−	4.29034i	−0.395517	−	0.228352i	0.289031	−	0.957320i	$-0.406667\pi$
$353$	−7.43108	−	4.29034i	−0.395517	−	0.228352i	−0.684548	+	0.728968i	$0.740000\pi$
$354$	−0.580723	−	0.468825i	−0.0308651	−	0.0249178i
$355$	2.81598	−	1.29492i	0.149457	−	0.0687274i
$356$	−7.03381	−	12.1829i	−0.372791	−	0.645693i
$357$	−4.02376	−	10.4356i	−0.212960	−	0.552310i
$358$	−14.8811	−	8.59160i	−0.786490	−	0.454080i
$359$	2.01575			0.106387			0.0531936	−	0.998584i	$-0.483060\pi$
$359$	2.01575			0.106387			0.0531936	+	0.998584i	$0.483060\pi$
$360$	14.7577	−	11.0669i	0.777799	−	0.583278i
$361$	33.9114			1.78481
$362$	7.17378	+	4.14178i	0.377045	+	0.217687i
$363$	−14.2909	−	2.24156i	−0.750078	−	0.117652i
$364$	−3.24016	−	5.61212i	−0.169831	−	0.294155i
$365$	8.46572	+	18.4098i	0.443116	+	0.963614i
$366$	−0.857526	+	5.46709i	−0.0448236	+	0.285769i
$367$	−6.87848	−	3.97129i	−0.359054	−	0.207300i	0.309612	−	0.950863i	$-0.399801\pi$
$367$	−6.87848	−	3.97129i	−0.359054	−	0.207300i	−0.668666	+	0.743563i	$0.733134\pi$
$368$			0.944508i			0.0492359i
$369$	10.0012	−	9.05943i	0.520643	−	0.471615i
$370$	2.01783	−	21.7320i	0.104902	−	1.12979i
$371$	−4.30040	+	7.44851i	−0.223265	+	0.386707i
$372$	0.791655	+	2.05315i	0.0410454	+	0.106451i
$373$	13.4710	−	7.77751i	0.697504	−	0.402704i	−0.108913	−	0.994051i	$-0.534737\pi$
$373$	13.4710	−	7.77751i	0.697504	−	0.402704i	0.806417	+	0.591347i	$0.201404\pi$
$374$	−4.36532	−	7.56096i	−0.225725	−	0.390968i
$375$	−11.1547	−	15.8295i	−0.576024	−	0.817433i
$376$	−2.71949	+	4.71029i	−0.140247	+	0.242915i
$377$		−	25.1437i		−	1.29497i
$378$	−0.245271	−	4.31014i	−0.0126154	−	0.221690i
$379$	21.7408			1.11675			0.558375	−	0.829589i	$-0.311425\pi$
$379$	21.7408			1.11675			0.558375	+	0.829589i	$0.311425\pi$
$380$	−17.3851	−	12.3115i	−0.891838	−	0.631567i
$381$	22.8698	+	18.4631i	1.17165	+	0.945891i
$382$	−13.5991	+	7.85144i	−0.695790	+	0.401714i
$383$	30.1124	−	17.3854i	1.53867	−	0.888352i	0.539754	−	0.841823i	$-0.318517\pi$
$383$	30.1124	−	17.3854i	1.53867	−	0.888352i	0.998917	−	0.0465296i	$-0.0148162\pi$
$384$	−13.1285	+	5.06211i	−0.669963	+	0.258325i
$385$	2.10299	−	2.96964i	0.107178	−	0.151347i
$386$	10.1971			0.519020
$387$	−8.60528	+	26.7562i	−0.437431	+	1.36010i
$388$		−	2.83964i		−	0.144161i
$389$	1.08700	−	1.88274i	0.0551132	−	0.0954588i	−0.837153	−	0.546969i	$-0.815781\pi$
$389$	1.08700	−	1.88274i	0.0551132	−	0.0954588i	0.892266	+	0.451511i	$0.149115\pi$
$390$	−3.91071	+	15.4334i	−0.198027	+	0.781498i
$391$	−9.10774	−	15.7751i	−0.460598	−	0.797779i
$392$	2.38141	−	1.37491i	0.120279	−	0.0694433i
$393$	32.1460	+	5.04218i	1.62155	+	0.254344i
$394$	6.76190	−	11.7120i	0.340660	−	0.590040i
$395$	1.07431	−	11.5703i	0.0540545	−	0.582165i
$396$	1.34811	+	6.25040i	0.0677449	+	0.314095i
$397$		−	22.9784i		−	1.15325i	−0.817008	−	0.576626i	$-0.804369\pi$
$397$		−	22.9784i		−	1.15325i	0.817008	−	0.576626i	$-0.195631\pi$
$398$	−15.5827	−	8.99667i	−0.781090	−	0.450962i
$399$	−11.7554	+	4.53265i	−0.588506	+	0.226916i
$400$	0.555820	+	1.57917i	0.0277910	+	0.0789586i
$401$	−10.3621	−	17.9477i	−0.517460	−	0.896267i	−0.999794	−	0.0202800i	$-0.993544\pi$
$401$	−10.3621	−	17.9477i	−0.517460	−	0.896267i	0.482334	−	0.875987i	$-0.339789\pi$
$402$	3.36693	−	4.17054i	0.167927	−	0.208008i
$403$	−4.15648	−	2.39975i	−0.207049	−	0.119540i
$404$	−21.8185			−1.08551
$405$	13.1929	−	15.1970i	0.655561	−	0.755143i
$406$	4.22205			0.209537
$407$	16.5569	+	9.55911i	0.820694	+	0.473828i
$408$	19.3191	−	23.9302i	0.956439	−	1.18472i
$409$	−11.0001	−	19.0527i	−0.543920	−	0.942097i	−0.998674	−	0.0514800i	$-0.983606\pi$
$409$	−11.0001	−	19.0527i	−0.543920	−	0.942097i	0.454754	−	0.890617i	$-0.349727\pi$
$410$	−3.49130	−	7.59229i	−0.172423	−	0.374957i
$411$	−10.4415	+	4.02602i	−0.515040	+	0.198589i
$412$	−1.41854	−	0.818996i	−0.0698866	−	0.0403490i
$413$		−	0.518645i		−	0.0255208i
$414$	−1.48239	−	6.87298i	−0.0728553	−	0.337788i
$415$	6.22087	+	0.577613i	0.305370	+	0.0283539i
$416$	14.2939	−	24.7577i	0.700815	−	1.21385i
$417$	23.7078	+	3.71863i	1.16098	+	0.182102i
$418$	−8.51721	+	4.91741i	−0.416590	+	0.240518i
$419$	−0.969751	−	1.67966i	−0.0473754	−	0.0820566i	0.841365	−	0.540467i	$-0.181752\pi$
$419$	−0.969751	−	1.67966i	−0.0473754	−	0.0820566i	−0.888741	+	0.458410i	$0.848419\pi$
$420$	4.91714	+	1.24597i	0.239932	+	0.0607972i
$421$	1.14152	−	1.97717i	0.0556341	−	0.0963612i	−0.836867	−	0.547406i	$-0.815615\pi$
$421$	1.14152	−	1.97717i	0.0556341	−	0.0963612i	0.892501	+	0.451045i	$0.148949\pi$
$422$		−	16.3909i		−	0.797896i
$423$	−1.81677	+	5.64886i	−0.0883346	+	0.274657i
$424$	−23.6506			−1.14857
$425$	−24.5109	−	21.0155i	−1.18895	−	1.01940i
$426$	1.86112	−	0.717609i	0.0901713	−	0.0347683i
$427$	−3.33037	+	1.92279i	−0.161168	+	0.0930503i
$428$	−8.23180	+	4.75263i	−0.397899	+	0.229727i
$429$	−10.8514	−	8.76045i	−0.523910	−	0.422959i
$430$	14.2040	+	10.0588i	0.684980	+	0.485078i
$431$	−24.3196			−1.17144			−0.585718	−	0.810515i	$-0.699187\pi$
$431$	−24.3196			−1.17144			−0.585718	+	0.810515i	$0.699187\pi$
$432$	−1.45486	+	0.954102i	−0.0699971	+	0.0459042i
$433$			24.2848i			1.16705i	0.812094	+	0.583527i	$0.198328\pi$
$433$			24.2848i			1.16705i	−0.812094	+	0.583527i	$0.801672\pi$
$434$	0.402958	−	0.697944i	0.0193426	−	0.0335024i
$435$	14.1053	+	13.7259i	0.676297	+	0.658109i
$436$	−1.42949	−	2.47596i	−0.0684603	−	0.118577i
$437$	−17.7702	+	10.2596i	−0.850062	+	0.490784i
$438$	4.69146	+	12.1673i	0.224166	+	0.581375i
$439$	−12.0889	+	20.9385i	−0.576970	+	0.999341i	0.418855	+	0.908053i	$0.362432\pi$
$439$	−12.0889	+	20.9385i	−0.576970	+	0.999341i	−0.995825	+	0.0912878i	$0.970902\pi$
$440$	9.96333	+	0.925103i	0.474983	+	0.0441026i
$441$	2.22342	−	2.01405i	0.105877	−	0.0959070i
$442$			26.5450i			1.26262i
$443$	−0.905401	−	0.522734i	−0.0430169	−	0.0248358i	0.478337	−	0.878176i	$-0.341240\pi$
$443$	−0.905401	−	0.522734i	−0.0430169	−	0.0248358i	−0.521354	+	0.853340i	$0.674573\pi$
$444$	−4.12973	+	26.3287i	−0.195988	+	1.24951i
$445$	−21.8208	+	10.0343i	−1.03441	+	0.475670i
$446$	−5.09900	−	8.83173i	−0.241445	−	0.418194i
$447$	1.70817	+	0.267931i	0.0807938	+	0.0126727i
$448$	3.57730	+	2.06536i	0.169012	+	0.0975790i
$449$	−7.38677			−0.348603			−0.174302	−	0.984692i	$-0.555767\pi$
$449$	−7.38677			−0.348603			−0.174302	+	0.984692i	$0.555767\pi$
$450$	−6.52305	−	10.6189i	−0.307500	−	0.500581i
$451$	7.32001			0.344686
$452$	4.30456	+	2.48524i	0.202469	+	0.116896i
$453$	0.724881	+	1.87998i	0.0340579	+	0.0883290i
$454$	5.74461	+	9.94996i	0.269608	+	0.466975i
$455$	−10.0519	+	4.62234i	−0.471239	+	0.216698i
$456$	−26.9567	−	21.7624i	−1.26236	−	1.01912i
$457$	−28.4023	−	16.3981i	−1.32860	−	0.767070i	−0.343520	−	0.939145i	$-0.611619\pi$
$457$	−28.4023	−	16.3981i	−1.32860	−	0.767070i	−0.985084	+	0.172075i	$0.944953\pi$
$458$			0.543122i			0.0253784i
$459$	15.0987	−	29.9643i	0.704747	−	1.39861i
$460$	8.22596	+	0.763787i	0.383538	+	0.0356118i
$461$	−9.87193	+	17.0987i	−0.459782	+	0.796365i	−0.998949	−	0.0458335i	$-0.985406\pi$
$461$	−9.87193	+	17.0987i	−0.459782	+	0.796365i	0.539168	+	0.842199i	$0.318739\pi$
$462$	1.47103	−	1.82213i	0.0684385	−	0.0847733i
$463$	1.08933	−	0.628922i	0.0506252	−	0.0292285i	−0.474474	−	0.880270i	$-0.657362\pi$
$463$	1.08933	−	0.628922i	0.0506252	−	0.0292285i	0.525099	+	0.851041i	$0.324028\pi$
$464$	−0.850750	−	1.47354i	−0.0394951	−	0.0684075i
$465$	3.61525	−	1.02171i	0.167653	−	0.0473807i
$466$	1.08255	−	1.87504i	0.0501483	−	0.0868594i
$467$		−	36.0058i		−	1.66615i	−0.553161	−	0.833074i	$-0.686579\pi$
$467$		−	36.0058i		−	1.66615i	0.553161	−	0.833074i	$-0.313421\pi$
$468$	5.95229	−	18.5073i	0.275144	−	0.855502i
$469$	3.72472			0.171991
$470$	2.99880	+	2.12364i	0.138324	+	0.0979564i
$471$	2.88207	−	18.3744i	0.132799	−	0.846646i
$472$	1.23510	−	0.713088i	0.0568503	−	0.0328225i
$473$	−13.2035	+	7.62304i	−0.607097	+	0.350508i
$474$	1.15880	−	7.38785i	0.0532256	−	0.339335i
$475$	−23.6733	+	27.6109i	−1.08621	+	1.26687i
$476$	8.45735			0.387642
$477$	−25.2224	+	5.44005i	−1.15485	+	0.249083i
$478$			22.2279i			1.01668i
$479$	16.4044	−	28.4133i	0.749537	−	1.29824i	−0.198508	−	0.980099i	$-0.563610\pi$
$479$	16.4044	−	28.4133i	0.749537	−	1.29824i	0.948045	−	0.318137i	$-0.103057\pi$
$480$	6.08573	+	21.5339i	0.277774	+	0.982885i
$481$	−29.0639	−	50.3401i	−1.32520	−	2.29531i
$482$	−14.3770	+	8.30059i	−0.654856	+	0.378082i
$483$	3.06913	−	3.80167i	0.139650	−	0.172982i
$484$	5.46924	−	9.47300i	0.248602	−	0.430591i
$485$	−4.82731	−	0.448219i	−0.219197	−	0.0203526i
$486$	9.08927	−	9.22616i	0.412298	−	0.418507i
$487$		−	19.2060i		−	0.870308i	−0.900356	−	0.435154i	$-0.856694\pi$
$487$		−	19.2060i		−	0.870308i	0.900356	−	0.435154i	$-0.143306\pi$
$488$	−9.15789	−	5.28731i	−0.414558	−	0.239345i
$489$	−8.13188	−	6.56497i	−0.367737	−	0.296878i
$490$	−0.776169	−	1.68788i	−0.0350637	−	0.0762507i
$491$	−3.39650	−	5.88291i	−0.153282	−	0.265492i	0.779150	−	0.626837i	$-0.215651\pi$
$491$	−3.39650	−	5.88291i	−0.153282	−	0.265492i	−0.932432	+	0.361345i	$0.882318\pi$
$492$	3.67103	+	9.52081i	0.165503	+	0.429231i
$493$	28.4183	+	16.4073i	1.27989	+	0.738947i
$494$	29.9022			1.34536
$495$	10.8383	−	1.30515i	0.487145	−	0.0586623i
$496$	−0.324787			−0.0145834
$497$	1.20041	+	0.693058i	0.0538458	+	0.0310879i
$498$	3.97214	+	0.623040i	0.177996	+	0.0279191i
$499$	−4.53988	−	7.86331i	−0.203233	−	0.352010i	0.746335	−	0.665570i	$-0.231812\pi$
$499$	−4.53988	−	7.86331i	−0.203233	−	0.352010i	−0.949568	+	0.313560i	$0.898478\pi$
$500$	14.2029	−	3.56376i	0.635172	−	0.159376i
$501$	0.477704	−	3.04556i	0.0213422	−	0.136066i
$502$	−7.56549	−	4.36794i	−0.337665	−	0.194951i
$503$		−	2.04265i		−	0.0910774i	−0.998963	−	0.0455387i	$-0.985500\pi$
$503$		−	2.04265i		−	0.0910774i	0.998963	−	0.0455387i	$-0.0145004\pi$
$504$	7.85327	+	2.52575i	0.349812	+	0.112506i
$505$	−3.44391	+	37.0908i	−0.153252	+	1.65052i
$506$	1.90699	−	3.30300i	0.0847759	−	0.146836i
$507$	7.15428	+	18.5546i	0.317733	+	0.824038i
$508$	−19.2480	+	11.1128i	−0.853990	+	0.493051i
$509$	−2.75003	−	4.76319i	−0.121893	−	0.211125i	0.798621	−	0.601834i	$-0.205563\pi$
$509$	−2.75003	−	4.76319i	−0.121893	−	0.211125i	−0.920514	+	0.390709i	$0.872230\pi$
$510$	−14.8914	−	14.4909i	−0.659402	−	0.641669i
$511$	−4.53095	+	7.84783i	−0.200437	+	0.347168i
$512$		−	3.77598i		−	0.166876i
$513$	−33.7539	−	17.0083i	−1.49027	−	0.750933i
$514$	−17.0253			−0.750954
$515$	−1.61618	+	2.28221i	−0.0712172	+	0.100566i
$516$	−16.5366	−	13.3502i	−0.727982	−	0.587709i
$517$	−2.78756	+	1.60940i	−0.122597	+	0.0707814i
$518$	8.45297	−	4.88032i	0.371402	−	0.214429i
$519$	−17.0107	+	6.55897i	−0.746685	+	0.287907i
$520$	−24.8281	−	17.5823i	−1.08878	−	0.771036i
$521$	−11.1250			−0.487397			−0.243699	−	0.969851i	$-0.578361\pi$
$521$	−11.1250			−0.487397			−0.243699	+	0.969851i	$0.578361\pi$
$522$	8.50341	+	9.38741i	0.372184	+	0.410876i
$523$			20.4936i			0.896122i	0.894003	+	0.448061i	$0.147885\pi$
$523$			20.4936i			0.896122i	−0.894003	+	0.448061i	$0.852115\pi$
$524$	−12.3025	+	21.3086i	−0.537438	+	0.930870i
$525$	2.89425	−	8.16231i	0.126315	−	0.356232i
$526$	4.52658	+	7.84027i	0.197368	+	0.341852i
$527$	5.42455	−	3.13187i	0.236297	−	0.136426i
$528$	−0.932359	−	0.146243i	−0.0405757	−	0.00636440i
$529$	−7.52129	+	13.0273i	−0.327013	+	0.566403i
$530$	−1.47726	+	15.9100i	−0.0641680	+	0.691087i
$531$	1.15317	−	1.04458i	0.0500432	−	0.0453307i
$532$		−	9.52697i		−	0.413046i
$533$	−19.2743	−	11.1280i	−0.834862	−	0.482008i
$534$	−14.4216	+	5.56070i	−0.624085	+	0.240635i
$535$	6.77999	+	14.7440i	0.293125	+	0.637438i
$536$	5.12113	+	8.87006i	0.221199	+	0.383128i
$537$	22.5021	−	27.8728i	0.971036	−	1.20280i
$538$	3.84074	+	2.21745i	0.165586	+	0.0956012i
$539$	1.62735			0.0700948
$540$	7.13303	+	13.4423i	0.306957	+	0.578465i
$541$	29.8258			1.28231			0.641156	−	0.767411i	$-0.278455\pi$
$541$	29.8258			1.28231			0.641156	+	0.767411i	$0.278455\pi$
$542$	−5.23071	−	3.01995i	−0.224678	−	0.129718i
$543$	−10.8476	+	13.4367i	−0.465517	+	0.576626i
$544$	18.6547	+	32.3108i	0.799813	+	1.38532i
$545$	−4.43469	+	2.03928i	−0.189961	+	0.0873532i
$546$	−6.64340	+	2.56156i	−0.284311	+	0.109625i
$547$	25.3903	+	14.6591i	1.08561	+	0.626777i	0.932404	−	0.361418i	$-0.117707\pi$
$547$	25.3903	+	14.6591i	1.08561	+	0.626777i	0.153205	+	0.988194i	$0.451041\pi$
$548$		−	8.46211i		−	0.361484i
$549$	−10.9827	−	3.53223i	−0.468730	−	0.150752i
$550$	1.24466	−	6.64467i	0.0530723	−	0.283330i
$551$	18.4823	−	32.0124i	0.787374	−	1.36377i
$552$	13.2731	+	2.08192i	0.564940	+	0.0886123i
$553$	4.50044	−	2.59833i	0.191378	−	0.110492i
$554$	1.91309	+	3.31357i	0.0812794	+	0.140780i
$555$	44.1062	+	11.1762i	1.87220	+	0.474405i
$556$	−9.07317	+	15.7152i	−0.384788	+	0.666472i
$557$		−	8.12407i		−	0.344228i	−0.985077	−	0.172114i	$-0.944940\pi$
$557$		−	8.12407i		−	0.344228i	0.985077	−	0.172114i	$-0.0550597\pi$
$558$	2.36340	−	0.509746i	0.100051	−	0.0215793i
$559$	46.3548			1.96060
$560$	−0.432689	+	0.611002i	−0.0182845	+	0.0258195i
$561$	16.9823	−	6.54805i	0.716995	−	0.276459i
$562$	3.29805	−	1.90413i	0.139120	−	0.0803208i
$563$	−13.7889	+	7.96103i	−0.581133	+	0.335517i	−0.761584	−	0.648067i	$-0.775578\pi$
$563$	−13.7889	+	7.96103i	−0.581133	+	0.335517i	0.180451	+	0.983584i	$0.442244\pi$
$564$	−3.49126	−	2.81853i	−0.147008	−	0.118682i
$565$	4.90427	−	6.92534i	0.206324	−	0.291351i
$566$	−17.5142			−0.736176
$567$	8.95616	+	0.887222i	0.376123	+	0.0372598i
$568$			3.81156i			0.159929i
$569$	−7.49692	+	12.9850i	−0.314287	+	0.544361i	−0.979286	−	0.202483i	$-0.935099\pi$
$569$	−7.49692	+	12.9850i	−0.314287	+	0.544361i	0.664999	+	0.746845i	$0.268432\pi$
$570$	−16.3236	+	16.7747i	−0.683721	+	0.702617i
$571$	−6.16600	−	10.6798i	−0.258039	−	0.446936i	0.707678	−	0.706535i	$-0.249743\pi$
$571$	−6.16600	−	10.6798i	−0.258039	−	0.446936i	−0.965716	+	0.259599i	$0.916410\pi$
$572$	9.13288	−	5.27287i	0.381865	−	0.220470i
$573$	−11.7773	−	30.5443i	−0.492003	−	1.27601i
$574$	1.86858	−	3.23648i	0.0779932	−	0.135088i
$575$	2.59683	−	13.8633i	0.108295	−	0.578141i
$576$	2.61270	+	12.1136i	0.108862	+	0.504733i
$577$			19.0064i			0.791246i	0.918413	+	0.395623i	$0.129471\pi$
$577$			19.0064i			0.791246i	−0.918413	+	0.395623i	$0.870529\pi$
$578$	−17.7702	−	10.2597i	−0.739145	−	0.426746i
$579$	−3.29413	+	21.0015i	−0.136899	+	0.872791i
$580$	−13.5214	+	6.21780i	−0.561447	+	0.258180i
$581$	1.39701	+	2.41970i	0.0579578	+	0.100386i
$582$	−3.08232	−	0.483470i	−0.127766	−	0.0200405i
$583$	−12.1213	−	6.99824i	−0.502013	−	0.289838i
$584$	−24.9185			−1.03114
$585$	−30.5224	−	13.0400i	−1.26194	−	0.539136i
$586$	7.81386			0.322788
$587$	20.9487	+	12.0947i	0.864644	+	0.499202i	0.865565	−	0.500797i	$-0.166960\pi$
$587$	20.9487	+	12.0947i	0.864644	+	0.499202i	−0.000920900		1.00000i	$0.500293\pi$
$588$	0.816126	+	2.11662i	0.0336565	+	0.0872879i
$589$	−3.52796	−	6.11060i	−0.145367	−	0.251783i
$590$	−0.402556	−	0.875410i	−0.0165730	−	0.0360401i
$591$	21.9369	+	17.7099i	0.902364	+	0.728490i
$592$	−3.40657	−	1.96678i	−0.140009	−	0.0808344i
$593$		−	18.5924i		−	0.763498i	−0.924266	−	0.381749i	$-0.875322\pi$
$593$		−	18.5924i		−	0.763498i	0.924266	−	0.381749i	$-0.124678\pi$
$594$	7.01409	−	0.399141i	0.287792	−	0.0163770i
$595$	1.33494	−	14.3772i	0.0547271	−	0.589409i
$596$	−0.653730	+	1.13229i	−0.0267778	+	0.0463806i
$597$	23.5630	−	29.1870i	0.964368	−	1.19454i
$598$	−10.0426	+	5.79808i	−0.410671	+	0.237101i
$599$	−21.3954	−	37.0579i	−0.874191	−	1.51414i	−0.857622	−	0.514281i	$-0.828059\pi$
$599$	−21.3954	−	37.0579i	−0.874191	−	1.51414i	−0.0165698	−	0.999863i	$-0.505275\pi$
$600$	23.4171	−	4.33002i	0.956000	−	0.176772i
$601$	14.3386	−	24.8352i	0.584885	−	1.01305i	−0.410005	−	0.912083i	$-0.634473\pi$
$601$	14.3386	−	24.8352i	0.584885	−	1.01305i	0.994890	−	0.100967i	$-0.0321936\pi$
$602$			7.78375i			0.317242i
$603$	7.50175	+	8.28162i	0.305495	+	0.337254i
$604$	−1.52360			−0.0619942
$605$	−15.2405	−	10.7928i	−0.619615	−	0.438789i
$606$	−3.71476	+	23.6831i	−0.150902	+	0.962062i
$607$	−3.11321	+	1.79741i	−0.126361	+	0.0729547i	−0.561848	−	0.827240i	$-0.689910\pi$
$607$	−3.11321	+	1.79741i	−0.126361	+	0.0729547i	0.435487	+	0.900195i	$0.356576\pi$
$608$	36.3972	−	21.0140i	1.47610	−	0.852229i
$609$	−1.36391	+	8.69551i	−0.0552685	+	0.352360i
$610$	−4.12886	+	5.83037i	−0.167173	+	0.236065i
$611$	9.78657			0.395922
$612$	17.0335	+	18.8043i	0.688539	+	0.760118i
$613$		−	11.4893i		−	0.464050i	−0.972710	−	0.232025i	$-0.925465\pi$
$613$		−	11.4893i		−	0.464050i	0.972710	−	0.232025i	$-0.0745351\pi$
$614$	0.749064	−	1.29742i	0.0302298	−	0.0523595i
$615$	16.7645	−	4.73785i	0.676011	−	0.191048i
$616$	2.23745	+	3.87538i	0.0901495	+	0.156143i
$617$	−2.45582	+	1.41787i	−0.0988676	+	0.0570812i	−0.548619	−	0.836073i	$-0.684846\pi$
$617$	−2.45582	+	1.41787i	−0.0988676	+	0.0570812i	0.449751	+	0.893154i	$0.351513\pi$
$618$	−1.13051	+	1.40033i	−0.0454756	+	0.0563296i
$619$	−11.8225	+	20.4772i	−0.475186	+	0.823047i	−0.999596	−	0.0284190i	$-0.990953\pi$
$619$	−11.8225	+	20.4772i	−0.475186	+	0.823047i	0.524410	+	0.851466i	$0.324286\pi$
$620$	−0.262643	+	2.82865i	−0.0105480	+	0.113601i
$621$	14.6341	−	0.832761i	0.587246	−	0.0334176i
$622$		−	4.48987i		−	0.180027i
$623$	−9.30190	−	5.37045i	−0.372673	−	0.215163i
$624$	2.23267	+	1.80246i	0.0893783	+	0.0721562i
$625$	−3.81645	−	24.7070i	−0.152658	−	0.988279i
$626$	10.3947	+	18.0042i	0.415457	+	0.719592i
$627$	−7.37620	−	19.1301i	−0.294577	−	0.763984i
$628$	12.1798	+	7.03201i	0.486027	+	0.280608i
$629$	75.8616			3.02480
$630$	2.18963	−	5.12522i	0.0872370	−	0.204194i
$631$	6.94839			0.276611			0.138306	−	0.990390i	$-0.455834\pi$
$631$	6.94839			0.276611			0.138306	+	0.990390i	$0.455834\pi$
$632$	12.3754	+	7.14491i	0.492265	+	0.284209i
$633$	33.7578	+	5.29500i	1.34175	+	0.210457i
$634$	−6.12421	−	10.6074i	−0.243224	−	0.421276i
$635$	15.8533	+	34.4750i	0.629118	+	1.36810i
$636$	3.02338	−	19.2753i	0.119885	−	0.764316i
$637$	−4.28497	−	2.47393i	−0.169776	−	0.0980205i
$638$			6.87075i			0.272015i
$639$	0.876725	+	4.06487i	0.0346827	+	0.160804i
$640$	−18.0874	−	1.67943i	−0.714965	−	0.0663851i
$641$	−9.24490	+	16.0126i	−0.365151	+	0.632461i	−0.988800	−	0.149244i	$-0.952316\pi$
$641$	−9.24490	+	16.0126i	−0.365151	+	0.632461i	0.623649	+	0.781705i	$0.285649\pi$
$642$	3.75727	+	9.74447i	0.148288	+	0.384583i
$643$	−4.01632	+	2.31883i	−0.158388	+	0.0914456i	−0.577099	−	0.816674i	$-0.695815\pi$
$643$	−4.01632	+	2.31883i	−0.158388	+	0.0914456i	0.418711	+	0.908120i	$0.362482\pi$
$644$	1.84729	+	3.19961i	0.0727935	+	0.126082i
$645$	−25.3051	+	26.0044i	−0.996387	+	1.02392i
$646$	−19.5124	+	33.7965i	−0.767705	+	1.32970i
$647$			19.1900i			0.754437i	0.926124	+	0.377219i	$0.123119\pi$
$647$			19.1900i			0.754437i	−0.926124	+	0.377219i	$0.876881\pi$
$648$	10.2010	+	22.5481i	0.400735	+	0.885774i
$649$	0.844015			0.0331305
$650$	−13.3787	+	15.6039i	−0.524754	+	0.612035i
$651$	1.30727	+	1.05538i	0.0512361	+	0.0413635i
$652$	6.84406	−	3.95142i	0.268034	−	0.154749i
$653$	−12.4992	+	7.21639i	−0.489130	+	0.282399i	−0.724213	−	0.689576i	$-0.757797\pi$
$653$	−12.4992	+	7.21639i	−0.489130	+	0.282399i	0.235084	+	0.971975i	$0.424464\pi$
$654$	−2.93094	+	1.13011i	−0.114609	+	0.0441908i
$655$	34.2821	+	24.2773i	1.33951	+	0.948593i
$656$	−1.50609			−0.0588029
$657$	−26.5746	+	5.73170i	−1.03677	+	0.223615i
$658$			1.64333i			0.0640637i
$659$	15.1138	−	26.1778i	0.588749	−	1.01974i	−0.405647	−	0.914030i	$-0.632954\pi$
$659$	15.1138	−	26.1778i	0.588749	−	1.01974i	0.994397	−	0.105714i	$-0.0337129\pi$
$660$	−2.02763	+	8.00189i	−0.0789254	+	0.311473i
$661$	−3.20680	−	5.55435i	−0.124730	−	0.216039i	0.796897	−	0.604115i	$-0.206473\pi$
$661$	−3.20680	−	5.55435i	−0.124730	−	0.216039i	−0.921627	+	0.388076i	$0.873140\pi$
$662$	−8.99597	+	5.19383i	−0.349638	+	0.201864i
$663$	−54.6706	−	8.57523i	−2.12323	−	0.333034i
$664$	−3.84152	+	6.65371i	−0.149080	+	0.258214i
$665$	−16.1956	−	1.50377i	−0.628037	−	0.0583137i
$666$	27.8757	+	8.96532i	1.08016	+	0.347399i
$667$			14.3350i			0.555054i
$668$	2.01881	+	1.16556i	0.0781100	+	0.0450968i
$669$	19.8366	−	7.64858i	0.766926	−	0.295711i
$670$	6.28687	−	2.89101i	0.242883	−	0.111689i
$671$	−3.12905	−	5.41967i	−0.120796	−	0.209224i
$672$	−6.28626	+	7.78666i	−0.242498	+	0.300377i
$673$	−19.8771	−	11.4760i	−0.766204	−	0.442368i	0.0653145	−	0.997865i	$-0.479195\pi$
$673$	−19.8771	−	11.4760i	−0.766204	−	0.442368i	−0.831519	+	0.555496i	$0.812528\pi$
$674$	−21.3574			−0.822655
$675$	23.9774	−	10.0041i	0.922892	−	0.385060i
$676$	−15.0373			−0.578356
$677$	29.4526	+	17.0045i	1.13196	+	0.653535i	0.944426	−	0.328724i	$-0.106619\pi$
$677$	29.4526	+	17.0045i	1.13196	+	0.653535i	0.187530	+	0.982259i	$0.439952\pi$
$678$	3.43051	−	4.24930i	0.131748	−	0.163193i
$679$	−1.08406	−	1.87765i	−0.0416025	−	0.0720576i
$680$	36.0735	−	16.5883i	1.38336	−	0.636133i
$681$	−22.3482	+	8.61701i	−0.856384	+	0.330205i
$682$	1.13580	+	0.655753i	0.0434920	+	0.0251101i
$683$			16.2790i			0.622898i	0.950263	+	0.311449i	$0.100814\pi$
$683$			16.2790i			0.622898i	−0.950263	+	0.311449i	$0.899186\pi$
$684$	21.1825	−	19.1878i	0.809932	−	0.733663i
$685$	−14.3853	−	1.33569i	−0.549635	−	0.0510341i
$686$	0.415414	−	0.719518i	0.0158606	−	0.0274713i
$687$	−1.11858	−	0.175453i	−0.0426767	−	0.00669394i
$688$	2.71661	−	1.56844i	0.103570	−	0.0597961i
$689$	21.2777	+	36.8541i	0.810617	+	1.40403i
$690$	2.22959	−	8.79892i	0.0848791	−	0.334969i
$691$	10.9933	−	19.0409i	0.418204	−	0.724350i	−0.577555	−	0.816352i	$-0.695993\pi$
$691$	10.9933	−	19.0409i	0.418204	−	0.724350i	0.995759	+	0.0920018i	$0.0293265\pi$
$692$		−	13.7860i		−	0.524065i
$693$	3.27756	+	3.61828i	0.124504	+	0.137447i
$694$	12.3580			0.469102
$695$	25.2832	+	17.9046i	0.959046	+	0.679162i
$696$	−22.5828	+	8.70748i	−0.855999	+	0.330056i
$697$	25.1545	−	14.5230i	0.952796	−	0.550097i
$698$	1.48537	−	0.857578i	0.0562220	−	0.0324598i
$699$	3.51201	+	2.83529i	0.132836	+	0.107240i
$700$	4.97147	+	4.26250i	0.187904	+	0.161107i
$701$	−33.8898			−1.28000			−0.639999	−	0.768376i	$-0.721065\pi$
$701$	−33.8898			−1.28000			−0.639999	+	0.768376i	$0.721065\pi$
$702$	−19.0756	−	9.61198i	−0.719961	−	0.362781i
$703$		−	85.4559i		−	3.22303i
$704$	−3.36105	+	5.82152i	−0.126675	+	0.219407i
$705$	−5.34249	+	5.49014i	−0.201210	+	0.206771i
$706$	−3.56453	−	6.17396i	−0.134153	−	0.232360i
$707$	−14.4270	+	8.32942i	−0.542583	+	0.313260i
$708$	0.423279	+	1.09777i	0.0159078	+	0.0412568i
$709$	−18.1485	+	31.4341i	−0.681582	+	1.18053i	0.292917	+	0.956138i	$0.405374\pi$
$709$	−18.1485	+	31.4341i	−0.681582	+	1.18053i	−0.974498	+	0.224396i	$0.927959\pi$
$710$	2.56408	+	0.238077i	0.0962282	+	0.00893487i
$711$	14.8413	+	4.77322i	0.556591	+	0.179010i
$712$		−	29.5355i		−	1.10689i
$713$	2.36971	+	1.36815i	0.0887464	+	0.0512377i
$714$	1.43993	−	9.18013i	0.0538879	−	0.343558i
$715$	−7.52215	−	16.3579i	−0.281312	−	0.611751i
$716$	13.5439	+	23.4587i	0.506158	+	0.876692i
$717$	−45.7793	−	7.18060i	−1.70966	−	0.268165i
$718$	1.45037	+	0.837371i	0.0541273	+	0.0312504i
$719$	0.810919			0.0302422			0.0151211	−	0.999886i	$-0.495187\pi$
$719$	0.810919			0.0302422			0.0151211	+	0.999886i	$0.495187\pi$
$720$	−2.22997	+	0.268535i	−0.0831062	+	0.0100077i
$721$	−1.25064			−0.0465762
$722$	24.3999	+	14.0873i	0.908070	+	0.524275i
$723$	−12.4510	−	32.2917i	−0.463058	−	1.20094i
$724$	−6.52914	−	11.3088i	−0.242653	−	0.420288i
$725$	8.43580	+	23.9674i	0.313298	+	0.890129i
$726$	−9.35139	−	7.54949i	−0.347063	−	0.280188i
$727$	−22.8173	−	13.1736i	−0.846247	−	0.488581i	0.0131356	−	0.999914i	$-0.495819\pi$
$727$	−22.8173	−	13.1736i	−0.846247	−	0.488581i	−0.859383	+	0.511333i	$0.829152\pi$
$728$		−	13.6057i		−	0.504259i
$729$	16.0655	+	21.7002i	0.595017	+	0.803713i
$730$	−1.55646	+	16.7630i	−0.0576071	+	0.620426i
$731$	−30.2484	+	52.3918i	−1.11878	+	1.93778i
$732$	5.47988	−	6.78781i	0.202542	−	0.250885i
$733$	−5.23418	+	3.02195i	−0.193329	+	0.111618i	−0.593540	−	0.804805i	$-0.702270\pi$
$733$	−5.23418	+	3.02195i	−0.193329	+	0.111618i	0.400211	+	0.916423i	$0.368937\pi$
$734$	−3.29946	−	5.71484i	−0.121785	−	0.210938i
$735$	3.72701	−	1.05329i	0.137473	−	0.0388513i
$736$	−8.14928	+	14.1150i	−0.300386	+	0.520284i
$737$			6.06141i			0.223275i
$738$	10.9595	−	2.36378i	0.403424	−	0.0870118i
$739$	52.8108			1.94268			0.971338	−	0.237704i	$-0.0763950\pi$
$739$	52.8108			1.94268			0.971338	+	0.237704i	$0.0763950\pi$
$740$	−19.8840	+	28.0782i	−0.730950	+	1.03218i
$741$	−9.65975	+	61.5849i	−0.354860	+	2.26238i
$742$	−6.18843	+	3.57289i	−0.227184	+	0.131165i
$743$	−26.6262	+	15.3727i	−0.976822	+	0.563968i	−0.901309	−	0.433176i	$-0.857393\pi$
$743$	−26.6262	+	15.3727i	−0.976822	+	0.563968i	−0.0755128	+	0.997145i	$0.524059\pi$
$744$	−0.715906	+	4.56420i	−0.0262464	+	0.167332i
$745$	1.82168	+	1.29005i	0.0667411	+	0.0472637i
$746$	12.9236			0.473165
$747$	−2.56636	+	7.97953i	−0.0938982	+	0.291956i
$748$			13.7631i			0.503227i
$749$	−3.62873	+	6.28514i	−0.132591	+	0.229654i
$750$	−1.45018	−	16.0234i	−0.0529531	−	0.585093i
$751$	0.841981	+	1.45835i	0.0307243	+	0.0532161i	0.880979	−	0.473156i	$-0.156885\pi$
$751$	0.841981	+	1.45835i	0.0307243	+	0.0532161i	−0.850254	+	0.526372i	$0.823552\pi$
$752$	0.573540	−	0.331134i	0.0209149	−	0.0120752i
$753$	11.4400	−	14.1704i	0.416896	−	0.516400i
$754$	10.4450	−	18.0913i	0.380386	−	0.658848i
$755$	−0.240490	+	2.59006i	−0.00875232	+	0.0942621i
$756$	−3.06242	+	6.07756i	−0.111379	+	0.221039i
$757$			12.2008i			0.443447i	0.975110	+	0.221724i	$0.0711683\pi$
$757$			12.2008i			0.443447i	−0.975110	+	0.221724i	$0.928832\pi$
$758$	15.6429	+	9.03144i	0.568176	+	0.328036i
$759$	6.18664	+	4.99454i	0.224561	+	0.181290i
$760$	−18.6863	−	40.6358i	−0.677822	−	1.47401i
$761$	−12.7596	−	22.1003i	−0.462536	−	0.801136i	0.536551	−	0.843868i	$-0.319727\pi$
$761$	−12.7596	−	22.1003i	−0.462536	−	0.801136i	−0.999087	+	0.0427323i	$0.986394\pi$
$762$	8.78542	+	22.7849i	0.318262	+	0.825411i
$763$	−1.89044	−	1.09145i	−0.0684385	−	0.0395130i
$764$	24.7541			0.895573
$765$	34.6553	−	25.9883i	1.25297	−	0.939610i
$766$	28.8886			1.04379
$767$	−2.22237	−	1.28309i	−0.0802453	−	0.0463296i
$768$	−25.6855	−	4.02883i	−0.926845	−	0.145378i
$769$	−10.9173	−	18.9094i	−0.393689	−	0.681889i	0.599244	−	0.800566i	$-0.295468\pi$
$769$	−10.9173	−	18.9094i	−0.393689	−	0.681889i	−0.992933	+	0.118678i	$0.962134\pi$
$770$	2.74677	−	1.26310i	0.0989867	−	0.0455188i
$771$	5.49994	−	35.0644i	0.198076	−	1.26281i
$772$	−13.9212	−	8.03742i	−0.501035	−	0.289273i
$773$			25.1482i			0.904517i	0.891887	+	0.452258i	$0.149381\pi$
$773$			25.1482i			0.904517i	−0.891887	+	0.452258i	$0.850619\pi$
$774$	−17.3066	+	15.6769i	−0.622072	+	0.563493i
$775$	4.76717	+	0.892969i	0.171242	+	0.0320764i
$776$	2.98097	−	5.16318i	0.107010	−	0.185348i
$777$	7.32056	+	18.9858i	0.262624	+	0.681113i
$778$	1.56424	−	0.903112i	0.0560806	−	0.0323781i
$779$	−16.3597	−	28.3359i	−0.586148	−	1.01524i
$780$	17.5036	−	17.9873i	0.626728	−	0.644049i
$781$	−1.12785	+	1.95349i	−0.0403575	+	0.0699012i
$782$		−	15.1339i		−	0.541188i
$783$	−22.0808	+	14.4806i	−0.789103	+	0.517495i
$784$	−0.334826			−0.0119581
$785$	13.8767	−	19.5953i	0.495281	−	0.699387i
$786$	21.0350	+	16.9818i	0.750295	+	0.605722i
$787$	−22.0797	+	12.7477i	−0.787056	+	0.454407i	−0.838925	−	0.544247i	$-0.816815\pi$
$787$	−22.0797	+	12.7477i	−0.787056	+	0.454407i	0.0518691	+	0.998654i	$0.483482\pi$
$788$	−18.4628	+	10.6595i	−0.657711	+	0.379729i
$789$	−17.6097	+	6.78994i	−0.626921	+	0.241728i
$790$	5.57946	−	7.87876i	0.198508	−	0.280314i
$791$	3.79505			0.134937
$792$	−4.11027	+	12.7800i	−0.146052	+	0.454118i
$793$			19.0274i			0.675681i
$794$	9.54555	−	16.5334i	0.338759	−	0.586748i
$795$	−32.2902	−	8.18214i	−1.14522	−	0.290190i
$796$	14.1824	+	24.5647i	0.502683	+	0.870672i
$797$	−11.5588	+	6.67345i	−0.409432	+	0.236386i	−0.690546	−	0.723289i	$-0.742630\pi$
$797$	−11.5588	+	6.67345i	−0.409432	+	0.236386i	0.281113	+	0.959675i	$0.409296\pi$
$798$	−10.3412	−	1.62204i	−0.366073	−	0.0574194i
$799$	−6.38614	+	11.0611i	−0.225925	+	0.391314i
$800$	−5.31889	+	28.3952i	−0.188051	+	1.00392i
$801$	−6.79368	−	31.4984i	−0.240043	−	1.11294i
$802$		−	17.2183i		−	0.607999i
$803$	−12.7712	−	7.37343i	−0.450684	−	0.260203i
$804$	−7.88380	+	3.03984i	−0.278040	+	0.107207i
$805$	5.73081	−	2.63530i	0.201985	−	0.0928823i
$806$	−1.99378	−	3.45332i	−0.0702278	−	0.121638i
$807$	−5.80768	+	7.19385i	−0.204440	+	0.253235i
$808$	−39.6715	−	22.9044i	−1.39564	−	0.805773i
$809$	−24.4319			−0.858981			−0.429490	−	0.903071i	$-0.641307\pi$
$809$	−24.4319			−0.858981			−0.429490	+	0.903071i	$0.641307\pi$
$810$	15.8056	−	5.45397i	0.555351	−	0.191633i
$811$	−15.5630			−0.546492			−0.273246	−	0.961944i	$-0.588097\pi$
$811$	−15.5630			−0.546492			−0.273246	+	0.961944i	$0.588097\pi$
$812$	−5.76398	−	3.32784i	−0.202276	−	0.116784i
$813$	7.90949	−	9.79731i	0.277398	−	0.343607i
$814$	7.94198	+	13.7559i	0.278366	+	0.482145i
$815$	−5.63700	−	12.2584i	−0.197455	−	0.429393i
$816$	−3.49411	+	1.34726i	−0.122318	+	0.0471635i
$817$	59.0178	+	34.0740i	2.06477	+	1.19210i
$818$		−	18.2784i		−	0.639089i
$819$	−3.12954	−	14.5099i	−0.109355	−	0.507017i
$820$	−1.21792	+	13.1169i	−0.0425315	+	0.458063i
$821$	0.0323750	−	0.0560751i	0.00112990	−	0.00195704i	−0.865460	−	0.500978i	$-0.832974\pi$
$821$	0.0323750	−	0.0560751i	0.00112990	−	0.00195704i	0.866590	+	0.499021i	$0.166307\pi$
$822$	−9.18529	−	1.44074i	−0.320374	−	0.0502515i
$823$	9.90397	−	5.71806i	0.345231	−	0.199319i	−0.317352	−	0.948308i	$-0.602794\pi$
$823$	9.90397	−	5.71806i	0.345231	−	0.199319i	0.662583	+	0.748989i	$0.269460\pi$
$824$	−1.71951	−	2.97828i	−0.0599020	−	0.103753i
$825$	13.2829	+	4.70995i	0.462452	+	0.163980i
$826$	0.215452	−	0.373174i	0.00749655	−	0.0129844i
$827$		−	23.7657i		−	0.826413i	−0.910637	−	0.413206i	$-0.864409\pi$
$827$		−	23.7657i		−	0.826413i	0.910637	−	0.413206i	$-0.135591\pi$
$828$	−3.39354	+	10.5515i	−0.117934	+	0.366689i
$829$	46.1598			1.60319			0.801597	−	0.597864i	$-0.203984\pi$
$829$	46.1598			1.60319			0.801597	+	0.597864i	$0.203984\pi$
$830$	4.23608	+	2.99984i	0.147037	+	0.104126i
$831$	−7.44247	+	2.86967i	−0.258176	+	0.0995476i
$832$	17.7000	−	10.2191i	0.613636	−	0.354283i
$833$	5.59223	−	3.22868i	0.193759	−	0.111867i
$834$	15.5135	+	12.5242i	0.537187	+	0.433677i
$835$	2.30007	−	3.24793i	0.0795972	−	0.112399i
$836$	15.5037			0.536206
$837$	0.286361	+	5.03221i	0.00989807	+	0.173939i
$838$		−	1.61139i		−	0.0556646i
$839$	5.41852	−	9.38515i	0.187068	−	0.324011i	−0.757203	−	0.653179i	$-0.773435\pi$
$839$	5.41852	−	9.38515i	0.187068	−	0.324011i	0.944271	+	0.329168i	$0.106768\pi$
$840$	7.63261	+	7.42734i	0.263350	+	0.256268i
$841$	1.58797	+	2.75045i	0.0547577	+	0.0948431i
$842$	1.64269	−	0.948405i	0.0566107	−	0.0326842i
$843$	2.85622	+	7.40760i	0.0983736	+	0.255131i
$844$	−12.9194	+	22.3770i	−0.444703	+	0.770248i
$845$	−2.37353	+	25.5629i	−0.0816520	+	0.879389i
$846$	−3.65382	+	3.30975i	−0.125621	+	0.113791i
$847$		−	8.35174i		−	0.286969i
$848$	2.49396	+	1.43989i	0.0856428	+	0.0494459i
$849$	5.65787	−	36.0713i	0.194178	−	1.23796i
$850$	−8.90595	−	25.3032i	−0.305471	−	0.867893i
$851$	16.5700	+	28.7001i	0.568013	+	0.983828i
$852$	−3.10643	−	0.487252i	−0.106425	−	0.0166930i
$853$	10.5649	+	6.09964i	0.361735	+	0.208848i	0.669841	−	0.742504i	$-0.266362\pi$
$853$	10.5649	+	6.09964i	0.361735	+	0.208848i	−0.308107	+	0.951352i	$0.599695\pi$
$854$	−3.19502			−0.109331
$855$	−29.2751	−	39.0382i	−1.00119	−	1.33508i
$856$	−19.9566			−0.682104
$857$	34.9698	+	20.1898i	1.19454	+	0.689671i	0.959334	−	0.282274i	$-0.0910886\pi$
$857$	34.9698	+	20.1898i	1.19454	+	0.689671i	0.235211	+	0.971944i	$0.424422\pi$
$858$	−4.16856	−	10.8111i	−0.142312	−	0.369086i
$859$	−8.22844	−	14.2521i	−0.280751	−	0.486275i	0.690819	−	0.723028i	$-0.257250\pi$
$859$	−8.22844	−	14.2521i	−0.280751	−	0.486275i	−0.971570	+	0.236753i	$0.923917\pi$
$860$	−11.4631	−	24.9280i	−0.390889	−	0.850039i
$861$	6.06205	+	4.89396i	0.206594	+	0.166786i
$862$	−17.4984	−	10.1027i	−0.595999	−	0.344100i
$863$			24.0438i			0.818461i	0.912431	+	0.409230i	$0.134203\pi$
$863$			24.0438i			0.818461i	−0.912431	+	0.409230i	$0.865797\pi$
$864$	−29.9739	+	1.70568i	−1.01973	+	0.0580284i
$865$	−23.4358	−	2.17603i	−0.796840	−	0.0739873i
$866$	−10.0883	+	17.4734i	−0.342813	+	0.593770i
$867$	26.8708	−	33.2843i	0.912581	−	1.13039i
$868$	−1.10024	+	0.635227i	−0.0373447	+	0.0215610i
$869$	4.22838	+	7.32377i	0.143438	+	0.248442i
$870$	4.44706	+	15.7356i	0.150770	+	0.533487i
$871$	9.21467	−	15.9603i	0.312227	−	0.540793i
$872$		−	6.00255i		−	0.203272i
$873$	1.99146	−	6.19200i	0.0674006	−	0.209568i
$874$	−17.0479			−0.576655
$875$	8.03083	−	7.77854i	0.271492	−	0.262963i
$876$	3.18547	−	20.3087i	0.107627	−	0.686167i
$877$	27.3431	−	15.7866i	0.923313	−	0.533075i	0.0386222	−	0.999254i	$-0.487703\pi$
$877$	27.3431	−	15.7866i	0.923313	−	0.533075i	0.884690	+	0.466179i	$0.154370\pi$
$878$	−17.3963	+	10.0438i	−0.587097	+	0.338961i
$879$	−2.52423	+	16.0930i	−0.0851401	+	0.542804i
$880$	−0.994313	−	0.704136i	−0.0335183	−	0.0237364i
$881$	7.34150			0.247341			0.123671	−	0.992323i	$-0.460533\pi$
$881$	7.34150			0.247341			0.123671	+	0.992323i	$0.460533\pi$
$882$	2.43646	−	0.525503i	0.0820398	−	0.0176946i
$883$		−	47.3972i		−	1.59504i	−0.603291	−	0.797521i	$-0.706144\pi$
$883$		−	47.3972i		−	1.59504i	0.603291	−	0.797521i	$-0.293856\pi$
$884$	20.9229	−	36.2395i	0.703712	−	1.21887i
$885$	1.93299	−	0.546285i	0.0649768	−	0.0183632i
$886$	−0.434302	−	0.752233i	−0.0145907	−	0.0252718i
$887$	−24.5759	+	14.1889i	−0.825179	+	0.476417i	−0.852199	−	0.523218i	$-0.824732\pi$
$887$	−24.5759	+	14.1889i	−0.825179	+	0.476417i	0.0270201	+	0.999635i	$0.491398\pi$
$888$	−35.1479	+	43.5370i	−1.17949	+	1.46101i
$889$	−8.48485	+	14.6962i	−0.284573	+	0.492894i
$890$	−19.8689	−	1.84484i	−0.666006	−	0.0618392i
$891$	−1.44382	+	14.5748i	−0.0483697	+	0.488274i
$892$			16.0762i			0.538271i
$893$	12.4600	+	7.19380i	0.416959	+	0.240731i
$894$	1.11776	+	0.902380i	0.0373835	+	0.0301801i
$895$	42.0168	−	19.3214i	1.40447	−	0.645842i
$896$	−4.06185	−	7.03533i	−0.135697	−	0.235034i
$897$	−8.69721	−	22.5562i	−0.290391	−	0.753128i
$898$	−5.31491	−	3.06857i	−0.177361	−	0.102399i
$899$	−4.92936			−0.164404
$900$	0.535448	+	19.6386i	0.0178483	+	0.654619i
$901$	−55.5384			−1.85025
$902$	5.26688	+	3.04084i	0.175368	+	0.101249i
$903$	−16.0310	−	2.51450i	−0.533478	−	0.0836774i
$904$	5.21784	+	9.03757i	0.173543	+	0.300585i
$905$	−20.2552	+	9.31431i	−0.673305	+	0.309618i
$906$	−0.259403	+	1.65380i	−0.00861809	+	0.0549439i
$907$	−5.68495	−	3.28221i	−0.188766	−	0.108984i	0.402639	−	0.915359i	$-0.368093\pi$
$907$	−5.68495	−	3.28221i	−0.188766	−	0.108984i	−0.591405	+	0.806375i	$0.701426\pi$
$908$		−	18.1117i		−	0.601058i
$909$	−47.5765	−	15.3014i	−1.57801	−	0.507517i
$910$	−9.15269	−	0.849835i	−0.303409	−	0.0281718i
$911$	1.16798	−	2.02300i	0.0386969	−	0.0670251i	−0.846028	−	0.533138i	$-0.821013\pi$
$911$	1.16798	−	2.02300i	0.0386969	−	0.0670251i	0.884725	+	0.466113i	$0.154346\pi$
$912$	1.51765	+	3.93602i	0.0502544	+	0.130335i
$913$	−3.93769	+	2.27342i	−0.130318	+	0.0752394i
$914$	−13.6240	−	23.5974i	−0.450642	−	0.780534i
$915$	−10.6741	−	10.3870i	−0.352875	−	0.343385i
$916$	0.428091	−	0.741475i	0.0141445	−	0.0244990i
$917$			18.7864i			0.620382i
$918$	23.3114	−	15.2877i	0.769391	−	0.504568i
$919$	39.7073			1.30982			0.654912	−	0.755706i	$-0.272706\pi$
$919$	39.7073			1.30982			0.654912	+	0.755706i	$0.272706\pi$
$920$	14.1551	+	10.0241i	0.466679	+	0.330485i
$921$	2.43011	+	1.96186i	0.0800748	+	0.0646454i
$922$	−14.2061	+	8.20188i	−0.467852	+	0.270114i
$923$	5.93946	−	3.42915i	0.195500	−	0.112872i
$924$	−3.44447	+	1.32812i	−0.113315	+	0.0436920i
$925$	44.5936	+	38.2342i	1.46623	+	1.25713i
$926$	1.04505			0.0343426
$927$	−2.51885	−	2.78070i	−0.0827298	−	0.0913301i
$928$		−	29.3613i		−	0.963832i
$929$	21.7027	−	37.5901i	0.712041	−	1.23329i	−0.252049	−	0.967715i	$-0.581104\pi$
$929$	21.7027	−	37.5901i	0.712041	−	1.23329i	0.964090	−	0.265577i	$-0.0855624\pi$
$930$	3.02568	+	0.766687i	0.0992158	+	0.0251407i
$931$	−3.63701	−	6.29949i	−0.119198	−	0.206457i
$932$	−2.95582	+	1.70655i	−0.0968212	+	0.0558997i
$933$	9.24709	+	1.45043i	0.302736	+	0.0474849i
$934$	14.9573	−	25.9068i	0.489418	−	0.847697i
$935$	23.3968	+	2.17241i	0.765156	+	0.0710454i
$936$	30.2512	−	27.4025i	0.988790	−	0.895677i
$937$			48.8313i			1.59525i	0.603154	+	0.797625i	$0.293910\pi$
$937$			48.8313i			1.59525i	−0.603154	+	0.797625i	$0.706090\pi$
$938$	2.68000	+	1.54730i	0.0875051	+	0.0505211i
$939$	−40.4384	+	15.5923i	−1.31966	+	0.508834i
$940$	−2.42013	−	5.26289i	−0.0789359	−	0.171656i
$941$	−20.7334	−	35.9114i	−0.675891	−	1.17068i	−0.976208	−	0.216837i	$-0.930426\pi$
$941$	−20.7334	−	35.9114i	−0.675891	−	1.17068i	0.300317	−	0.953839i	$-0.402907\pi$
$942$	9.70667	−	12.0234i	0.316260	−	0.391745i
$943$	10.9887	+	6.34435i	0.357843	+	0.206600i
$944$	−0.173656			−0.00565202
$945$	9.84829	+	6.16533i	0.320365	+	0.200558i
$946$	−12.6669			−0.411836
$947$	10.2602	+	5.92375i	0.333413	+	0.192496i	0.657355	−	0.753581i	$-0.271675\pi$
$947$	10.2602	+	5.92375i	0.333413	+	0.192496i	−0.323942	+	0.946077i	$0.605008\pi$
$948$	−7.40514	+	9.17259i	−0.240508	+	0.297912i
$949$	22.4185	+	38.8299i	0.727734	+	1.26047i
$950$	−28.5033	+	10.0323i	−0.924770	+	0.325491i
$951$	23.8249	−	9.18642i	0.772576	−	0.297890i
$952$	15.3776	+	8.87826i	0.498391	+	0.287746i
$953$			13.9964i			0.453388i	0.973966	+	0.226694i	$0.0727918\pi$
$953$			13.9964i			0.453388i	−0.973966	+	0.226694i	$0.927208\pi$
$954$	−20.4078	−	6.56352i	−0.660728	−	0.212502i
$955$	3.90728	−	42.0813i	0.126437	−	1.36172i
$956$	17.5201	−	30.3457i	0.566640	−	0.981450i
$957$	−14.1506	−	2.21956i	−0.457425	−	0.0717482i
$958$	23.6066	−	13.6293i	0.762693	−	0.440341i
$959$	−3.23049	−	5.59538i	−0.104318	−	0.180684i
$960$	−3.92964	+	15.5081i	−0.126829	+	0.500520i
$961$	15.0295	−	26.0319i	0.484824	−	0.839739i
$962$		−	48.2942i		−	1.55707i
$963$	−21.2830	+	4.59038i	−0.685833	+	0.147923i
$964$	26.1702			0.842886
$965$	−15.8607	+	22.3970i	−0.510575	+	0.720984i
$966$	3.78756	−	1.46041i	0.121863	−	0.0469879i
$967$	25.3957	−	14.6622i	0.816671	−	0.471505i	−0.0325964	−	0.999469i	$-0.510378\pi$
$967$	25.3957	−	14.6622i	0.816671	−	0.471505i	0.849267	+	0.527964i	$0.177044\pi$
$968$	19.8889	−	11.4829i	0.639253	−	0.369073i
$969$	−63.3020	−	51.1045i	−2.03355	−	1.64171i
$970$	−3.28714	−	2.32783i	−0.105544	−	0.0747422i
$971$	22.3105			0.715978			0.357989	−	0.933726i	$-0.383463\pi$
$971$	22.3105			0.715978			0.357989	+	0.933726i	$0.383463\pi$
$972$	−19.6809	+	5.43144i	−0.631264	+	0.174214i
$973$			13.8551i			0.444173i
$974$	7.97845	−	13.8191i	0.255646	−	0.442792i
$975$	−27.8151	−	32.5947i	−0.890795	−	1.04387i
$976$	0.643801	+	1.11510i	0.0206076	+	0.0356933i
$977$	−27.1071	+	15.6503i	−0.867232	+	0.500696i	−0.866427	−	0.499303i	$-0.833589\pi$
$977$	−27.1071	+	15.6503i	−0.867232	+	0.500696i	−0.000804405		1.00000i	$0.500256\pi$
$978$	−3.12386	−	8.10172i	−0.0998900	−	0.259064i
$979$	8.73959	−	15.1374i	0.279319	−	0.483794i
$980$	−0.270761	+	2.91609i	−0.00864915	+	0.0931511i
$981$	−1.38069	−	6.40147i	−0.0440821	−	0.204383i
$982$		−	5.64382i		−	0.180101i
$983$	−24.9825	−	14.4237i	−0.796819	−	0.460044i	0.0455386	−	0.998963i	$-0.485500\pi$
$983$	−24.9825	−	14.4237i	−0.796819	−	0.460044i	−0.842358	+	0.538919i	$0.818833\pi$
$984$	−3.31978	+	21.1649i	−0.105831	+	0.674714i
$985$	15.2066	+	33.0688i	0.484523	+	1.05366i
$986$	13.6316	+	23.6107i	0.434120	+	0.751918i
$987$	−3.38452	−	0.530870i	−0.107730	−	0.0168978i
$988$	−40.8227	−	23.5690i	−1.29874	−	0.749830i
$989$	−26.4280			−0.840360
$990$	8.34052	+	3.56329i	0.265079	+	0.113249i
$991$	−22.2547			−0.706943			−0.353472	−	0.935445i	$-0.614999\pi$
$991$	−22.2547			−0.706943			−0.353472	+	0.935445i	$0.614999\pi$
$992$	−4.85370	−	2.80228i	−0.154105	−	0.0889726i
$993$	−7.79082	−	20.2055i	−0.247234	−	0.641201i
$994$	0.575812	+	0.997335i	0.0182636	+	0.0316336i
$995$	43.9978	−	20.2323i	1.39482	−	0.641407i
$996$	−4.93172	−	3.98143i	−0.156267	−	0.126157i
$997$	32.1153	+	18.5418i	1.01710	+	0.587223i	0.913263	−	0.407371i	$-0.133554\pi$
$997$	32.1153	+	18.5418i	1.01710	+	0.587223i	0.103838	+	0.994594i	$0.466888\pi$
$998$		−	7.54372i		−	0.238792i
$999$	−27.4696	+	54.5151i	−0.869099	+	1.72478i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	315.2.bh.c.169.20	yes	64
3.2	odd	2		945.2.bh.c.694.13		64
5.4	even	2	inner	315.2.bh.c.169.13	✓	64
9.4	even	3	inner	315.2.bh.c.274.13	yes	64
9.5	odd	6		945.2.bh.c.64.20		64
15.14	odd	2		945.2.bh.c.694.20		64
45.4	even	6	inner	315.2.bh.c.274.20	yes	64
45.14	odd	6		945.2.bh.c.64.13		64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
315.2.bh.c.169.13	✓	64	5.4	even	2	inner
315.2.bh.c.169.20	yes	64	1.1	even	1	trivial
315.2.bh.c.274.13	yes	64	9.4	even	3	inner
315.2.bh.c.274.20	yes	64	45.4	even	6	inner
945.2.bh.c.64.13		64	45.14	odd	6
945.2.bh.c.64.20		64	9.5	odd	6
945.2.bh.c.694.13		64	3.2	odd	2
945.2.bh.c.694.20		64	15.14	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 315 = 3^{2} \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	315.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.719518 + 0.415414i) q^{2} +(-1.08800 + 1.34768i) q^{3} +(-0.654862 - 1.13425i) q^{4} +(-2.03156 + 0.934211i) q^{5} +(-1.34268 + 0.517712i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.74981i q^{8} +(-0.632505 - 2.93256i) q^{9} +O(q^{10})\)	\(q+(0.719518 + 0.415414i) q^{2} +(-1.08800 + 1.34768i) q^{3} +(-0.654862 - 1.13425i) q^{4} +(-2.03156 + 0.934211i) q^{5} +(-1.34268 + 0.517712i) q^{6} +(-0.866025 - 0.500000i) q^{7} -2.74981i q^{8} +(-0.632505 - 2.93256i) q^{9} +(-1.84983 - 0.171758i) q^{10} +(0.813674 - 1.40932i) q^{11} +(2.24111 + 0.351523i) q^{12} +(-4.28497 + 2.47393i) q^{13} +(-0.415414 - 0.719518i) q^{14} +(0.951323 - 3.75433i) q^{15} +(-0.167413 + 0.289968i) q^{16} -6.45735i q^{17} +(0.763130 - 2.37279i) q^{18} -7.27402 q^{19} +(2.39003 + 1.69253i) q^{20} +(1.61608 - 0.623128i) q^{21} +(1.17091 - 0.676023i) q^{22} +(2.44296 - 1.41044i) q^{23} +(3.70588 + 2.99180i) q^{24} +(3.25450 - 3.79582i) q^{25} -4.11082 q^{26} +(4.64034 + 2.33822i) q^{27} +1.30972i q^{28} +(-2.54087 + 4.40091i) q^{29} +(2.24410 - 2.30612i) q^{30} +(0.485008 + 0.840058i) q^{31} +(-5.00373 + 2.88890i) q^{32} +(1.01405 + 2.62992i) q^{33} +(2.68248 - 4.64619i) q^{34} +(2.22649 + 0.206732i) q^{35} +(-2.91207 + 2.63785i) q^{36} +11.7481i q^{37} +(-5.23379 - 3.02173i) q^{38} +(1.32798 - 8.46641i) q^{39} +(2.56890 + 5.58642i) q^{40} +(2.24906 + 3.89549i) q^{41} +(1.42165 + 0.222990i) q^{42} +(-8.11350 - 4.68433i) q^{43} -2.13138 q^{44} +(4.02461 + 5.36680i) q^{45} +2.34367 q^{46} +(-1.71295 - 0.988971i) q^{47} +(-0.208640 - 0.541106i) q^{48} +(0.500000 + 0.866025i) q^{49} +(3.91851 - 1.37919i) q^{50} +(8.70247 + 7.02561i) q^{51} +(5.61212 + 3.24016i) q^{52} -8.60079i q^{53} +(2.36748 + 3.61005i) q^{54} +(-0.336424 + 3.62328i) q^{55} +(-1.37491 + 2.38141i) q^{56} +(7.91415 - 9.80309i) q^{57} +(-3.65640 + 2.11103i) q^{58} +(0.259322 + 0.449159i) q^{59} +(-4.88135 + 1.37952i) q^{60} +(1.92279 - 3.33037i) q^{61} +0.805916i q^{62} +(-0.918517 + 2.85593i) q^{63} -4.13071 q^{64} +(6.39401 - 9.02900i) q^{65} +(-0.362883 + 2.31353i) q^{66} +(-3.22570 + 1.86236i) q^{67} +(-7.32428 + 4.22868i) q^{68} +(-0.757112 + 4.82691i) q^{69} +(1.51612 + 1.07366i) q^{70} -1.38612 q^{71} +(-8.06400 + 1.73927i) q^{72} -9.06190i q^{73} +(-4.88032 + 8.45297i) q^{74} +(1.57466 + 8.51589i) q^{75} +(4.76348 + 8.25060i) q^{76} +(-1.40932 + 0.813674i) q^{77} +(4.47257 - 5.54008i) q^{78} +(-2.59833 + 4.50044i) q^{79} +(0.0692192 - 0.745488i) q^{80} +(-8.19987 + 3.70972i) q^{81} +3.73717i q^{82} +(-2.41970 - 1.39701i) q^{83} +(-1.76509 - 1.42498i) q^{84} +(6.03253 + 13.1185i) q^{85} +(-3.89188 - 6.74093i) q^{86} +(-3.16657 - 8.21249i) q^{87} +(-3.87538 - 2.23745i) q^{88} +10.7409 q^{89} +(0.666335 + 5.53339i) q^{90} +4.94785 q^{91} +(-3.19961 - 1.84729i) q^{92} +(-1.65982 - 0.260347i) q^{93} +(-0.821665 - 1.42317i) q^{94} +(14.7776 - 6.79547i) q^{95} +(1.55073 - 9.88658i) q^{96} +(1.87765 + 1.08406i) q^{97} +0.830828i q^{98} +(-4.64759 - 1.49475i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9}+O(q^{10}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9	\( 64 q + 34 q^{4} - 10 q^{5} - 18 q^{6} - 14 q^{9} - 4 q^{10} + 18 q^{11} - 6 q^{14} - 14 q^{15} - 46 q^{16} + 48 q^{19} - 2 q^{20} - 2 q^{21} - 12 q^{24} + 18 q^{25} - 12 q^{26} - 30 q^{29} - 4 q^{30} - 4 q^{31} + 34 q^{34} + 8 q^{35} - 42 q^{36} - 8 q^{39} - 6 q^{40} + 28 q^{41} + 68 q^{44} - 6 q^{45} - 24 q^{46} + 32 q^{49} - 58 q^{50} + 62 q^{51} + 54 q^{54} - 12 q^{55} + 18 q^{56} + 16 q^{59} - 66 q^{60} + 40 q^{61} - 100 q^{64} - 18 q^{65} - 146 q^{66} - 20 q^{69} - 4 q^{70} - 176 q^{71} - 20 q^{74} + 60 q^{75} - 22 q^{79} + 64 q^{80} - 58 q^{81} - 4 q^{84} - 14 q^{85} + 60 q^{86} - 200 q^{89} + 8 q^{90} - 16 q^{91} - 42 q^{94} + 68 q^{95} + 210 q^{96} + 90 q^{99}+O(q^{100}) \) 64 * q + 34 * q^4 - 10 * q^5 - 18 * q^6 - 14 * q^9 - 4 * q^10 + 18 * q^11 - 6 * q^14 - 14 * q^15 - 46 * q^16 + 48 * q^19 - 2 * q^20 - 2 * q^21 - 12 * q^24 + 18 * q^25 - 12 * q^26 - 30 * q^29 - 4 * q^30 - 4 * q^31 + 34 * q^34 + 8 * q^35 - 42 * q^36 - 8 * q^39 - 6 * q^40 + 28 * q^41 + 68 * q^44 - 6 * q^45 - 24 * q^46 + 32 * q^49 - 58 * q^50 + 62 * q^51 + 54 * q^54 - 12 * q^55 + 18 * q^56 + 16 * q^59 - 66 * q^60 + 40 * q^61 - 100 * q^64 - 18 * q^65 - 146 * q^66 - 20 * q^69 - 4 * q^70 - 176 * q^71 - 20 * q^74 + 60 * q^75 - 22 * q^79 + 64 * q^80 - 58 * q^81 - 4 * q^84 - 14 * q^85 + 60 * q^86 - 200 * q^89 + 8 * q^90 - 16 * q^91 - 42 * q^94 + 68 * q^95 + 210 * q^96 + 90 * q^99

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